Criteria
4.3 HEARING DAMAGE RISK
4.3.4 Alternative Formulations
The authors have demonstrated that an alternative interpretation of the International Standard ISO 1999 data base is possible, and that the interpretation put upon it by the standard is not unique (Bies and Hansen, 1990). Alternatively, very extensive work
H) ' 10 log10(STA%STN) (4.26)
STA ' 10H/ 10 (4.27)
carried out in Dresden, Germany, over a period of about two decades between the mid- 1960s and mid-1980s has provided yet a third interpretation of the existing data base.
These latter two formulations lead to the conclusion that for the purpose of determining hearing loss, noise exposure should be determined as an integral of the root mean square (r.m.s.) pressure with time rather than the accepted integral of mean square pressure. This in turn leads to a 6 dB trading rule rather than the 3 dB trading rule that is widely accepted. Trading rules are discussed below in Section 4.3.6.
Recently, it has been shown that neither the formulation of Bies and Hansen nor the standard, ISO 1999, accounts for post exposure loss observed in war veterans (Macrae, 1991). Similarly it may be shown that the formulation of the Dresden group (Kraak et al., 1977, Kraak, 1981) does not account for the observed loss. However, the formulation of Bies and Hansen (1990) as well as that of the Dresden group may be amended to successfully account for post-exposure loss (Bies, 1994).
4.3.4.1 Bies and Hansen Formulation
Bies and Hansen (1990) introduce sensitivity associated with age, STA and with noise, STN (as amended by Bies (1994)) and they propose that the effects of age and noise may be additive on a hearing sensitivity basis. They postulate the following relationship describing hearing loss, H), with increasing age and exposure to noise, which may be contrasted with the ISO 1999 formulation embodied in Equation (4.16):
Additivity of effects on a sensitivity basis rather than on a logarithmic basis (which implies multiplication of effects) is proposed.
Hearing sensitivity associated with age is defined as follows:
In the above equations, H is the observed hearing loss in a population unexposed to excessive noise, called presbyacusis, and is due to aging alone. It may be calculated by using Equation (4.22).
Bies and Hansen (1990) proposed an empirically determined expression for the sensitivity to noise, STN. Their expression, modified according to Bies (1994), accounts for both loss at the time of cessation of exposure to excessive noise, STN(Yns) where Yns (years) is the age when exposure to excessive noise stopped and to post- exposure loss, Mc , after exposure to excessive noise has stopped. The former term, STN(Yns), accounts for loss up to cessation of exposure at Yns years, while the latter term, Mc accounts for continuing hearing loss after exposure to excessive noise ceases.
Loss at the cessation of exposure is a function of the length of exposure, Θ = Y ! 18 (years) and the A-weighted sound pressure of the excessive noise, pA. Here, Y is the age of the population and following the international standard ISO 1999 it is assumed that exposure to excessive noise begins at age 18 years. The quantity STN is defined as zero when Θ is zero. Use of Equations (4.16), (4.26) and (4.27) gives the
STN(Yns) ' 10H/ 10 10(N&0 0083HN) / 10&1 (4.28)
STN ' STN(Yns)%Mc(Yns,Y)
Y >Yns (4.29)
Mc ' 0.0208Yns(Y & Yns) (4.30)
pA ' 10LAeq) / 20 (4.31)
LAeq) ' 20 log10 1 Tm
T
0
pA2(t)1/2dt (4.32)
following expression for STN(Yns) in terms of N given by Equation (4.17) or (4.18) and H given by Equation (4.22):
Hearing sensitivity, STN, associated with noise exposure is then:
The post-exposure term, Mc , has been determined empirically for one frequency (Bies, 1994) and may be expressed in terms of the age of the population, Y, and the age when exposure to excessive noise, Yns, stopped. The proposed post-exposure correction is based upon data provided by Macrae (1991) and is limited to loss at 4 kHz as no information is available for other frequencies:
For the case of the reconstructed data base of the International Standard, the quantity, Mcis assumed to be zero, because the standard provides no post-exposure information.
Implicit in this formulation is the assumption that the A-weighted sound pressure, pA is determined in terms of the equivalent A-weighted sound pressure level, LAeq) as follows:
where
which may be contrasted with the traditional Equation (4.1). Equation (4.32) implies that an equivalent noise level may be calculated by integrating acoustic pressures rather than pressures squared as implied by Equation (4.1). This leads to a 6 dB trading rule for exposure time versus exposure level (see Section 4.3.6).
4.3.4.2 Dresden Group Formulation
The Dresden group investigated the relationship between noise exposure and hearing loss using retrospective studies of noise exposed persons, temporary threshold shift investigations, and animal experiments. Their major result supported by all three types of investigation describing the long-term effect of noise on the average hearing loss of an exposed population is summarised for the 4 kHz frequency below. The
Bs ' m
Ts
0
pA2(t)1/2dt (4.33)
Ba ' 0.025 (Tsa&Ts) (4.34)
H) ' kflog10 Bs%Ba
B0 (4.35)
relationship describes exposure to all kinds of industrial and other noise including interrupted, fluctuating, and impulsive noise with peak sound pressure levels up to 135 dB re 20 µPa. At higher levels, the observed loss seems to be dependent upon pressure squared or energy input.
An A-weighted linear noise dose, Bs is defined in terms of the total time, Ts of exposure to noise in seconds as follows:
An age-related noise dose, Ba in terms of the age of the person, Tsa in seconds is defined as follows:
The permanent threshold shift, HN , is given by the following equation:
The quantities of Equation (4.35), not already defined, are kf , a constant specific for each audiometric frequency, with the value of 50 for 4 kHz and B0 , a critical noise dose used as a reference with the value of 2 × 107 Pa s.
Consideration of Equation (4.35) shows that if the term associated with noise exposure, Bs is very much larger than the term associated with age, Ba, then with cessation of exposure to noise, no further threshold shift should be observed until the term associated with age also becomes large. However, as pointed out above, Macrae (1991) has provided data showing the threshold shift continues and as suggested above, the expression given by Equation (4.35) may be corrected by the simple device of adding Mc, given by Equation (4.30).