use of a loudness model for hearing-aid fitting. i. linear hearing aids

British Journal of Audiology, 1998,32,317-335

Use of a loudness model for hearing-aid fitting. I. Linear hearing aids

Brian C.J. Moore and Brian R. Glasberg

Department of Experimental Psychology, University of Cambridge, Cambridge

(Received 22 October 1997, accepted 4 February 1998)

Abstract A model for predicting loudness for people with cochlear hearing loss is applied to the problem of prescribing the frequency-gain characteristic of a linear hearing aid. It is argued that a reasonable goal is to make all frequency bands of speech equally loud while achieving a comfortable overall loudness; this can maximize the proportion of the speech spectrum that is above the absolute threshold for a given loudness. In terms of the model this means that the specific loudness pattern evoked by speech of a moderate level (65 dB SPL) should be reasonably flat (equal loudness per critical band), and the overall loudness should be similar to that evoked in a normal listener by 65 dB speech (about 23 sones). The model is used to develop a new formula - the ‘Cambridge formula’ - for prescribing insertion gain from audiometric thresholds. It is shown that, for a fixed overall loudness of 23 sones, the Cambridge formula leads to a higher calculated articulation index than three other commonly used prescriptive methods: NAL(R), FIG6 and DSL.

Key words: hearing aids, hearing loss, prescriptive methods, loudness, articulation index

Introduction Models for predicting the loudness of sounds for normally hearing persons have been developed and refined over many years (Fletcher and Mun- son, 1933; Zwicker, 1958; Zwicker and Scharf, 1965; Stevens, 1972; Zwicker and Fastl, 1990; Moore and Glasberg, 1996; Moore et al., 1997a). More recently, the models have been extended to attempt to account for loudness perception by people with cochlear hearing loss (Florentine and Zwicker, 1979; Launer, 1995; Florentine et al., 1997; Moore and Glasberg, 1997). This paper describes an application of a specific loudness model (Moore and Glasberg, 1997) to the derivation of a prescription formula for linear hearing aids, i.e. aids not incorporating any form of compression (except for high-level limiting), and for aids incorporating slow-acting automatic gain control, such as the dual front-end AGC system Address for correspondence: Professor Brian C.J. Moore, Department of Experimental Psychology, University of Cambridge, Downing Street, Cambridge CB2 3EB.

developed at Cambridge (Moore and Glasberg, 1988; Moore et al., 1991; Moore, 1993). In subse- quent papers we plan to describe applications of the model to the fitting of hearing aids with multi-band compression. We start by giving a description of the loudness model and of the con- cepts underlying it.

The loudness model The model developed at Cambridge (Moore and Glasberg, 1997) has four stages. The first stage is a fixed filter to account for the transmission of sound through the outer and middle ear. The next stage is the calculation of an excitation pattern for the sound under consideration; for a detailed description of the concept of the excitation pattern, see Moore (1997). Briefly, the excitation pattern can be thought of as representing the distribution of excitation at different points along the basilar membrane (BM). The excitation patterns are calculated from auditory filter shapes, which represent frequency selectivity at a

030&5364/98/3203 17+18 $03.50/0 0 1998 British Society of Audiology

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318 B.C.J. Moore and B.R. Glasberg

specific centre frequency. The auditory filter shapes are derived from psychoacoustical experi- ments on masking (Glasberg and Moore, 1990). The frequency scale of the excitation pattern is translated to a scale that is related to how the sound is represented in the auditory system. This scale is based on the equivalent rectangular bandwidth (ERB) of the auditory filter, which is closely related to the ‘critical bandwidth’ (Zwicker, 1961; Scharf, 1970); each ERB corresponds roughly to a constant distance of about 0.89 mm along the BM (Greenwood, 1961; Moore, 1986; Greenwood, 1990). Excitation patterns of a 1000 Hz sinusoid for a normal ear are plotted in panel A of Fig. 1 for levels of the sinusoid from 20 to 100 dB SPL. The scale at the top of the figure shows the frequency corresponding to the number of ERBs at the bottom of the figure.

The next stage is a transformation from excitation level to specific loudness, N , which is the loudness per ERB. The specific loudness is a kind of loudness density. It represents the loudness that would be evoked by the excitation within a 0.89 mm range on the BM if it were possible to present that excitation alone (without any excitation at adjacent regions on the BM). There is a compressive relationship between excitation and

Frequency (Hz)

250 500 1000 2000 4000 8000

- a, a, - C

m 0

._ .... c ._

lz

specific loudness; when the excitation is doubled, the specific loudness grows by less than a factor of two. In fact, for values of the excitation well above the threshold value, the specific loudness grows by a factor of only about 1.15 when the excitation is doubled. The relationship between excitation and specific loudness is plotted in Fig. 2 for a series of values of the excitation level at absolute threshold, L,,,. The value of N is plotted on a logarithmic scale as a function of excitation level in decibels (also a log scale). The steepness of the initial part of the curves depends on the value of L,,,,; the higher E,,,, the steeper the curve. Thus the functions show a recruitment-like effect, since higher thresholds are associated with steeper functions.

The compressive non-linearity in the model can be thought of as representing the overall effects of the transformation from the physical stimulus to neural activity. At least two non-lin- earities contribute to this overall effect: the compressive non-linearity of the BM input-output function, and the non-linear transformation from BM velocity or amplitude to neural activity (Yates, 1990).

If the specific loudness is plotted as a function of frequency or number of ERBs, the resulting

Frequency (Hz)

250 500 1000 2000 4000 8000

1

m

Y II:

a, 0

5 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 Number of ERBs Number of ERBs

Fig. 1. The left panel (A) shows excitation patterns for a I kHz sinusoid with level ranging from 20 d B (lowest curve) to 100 d B (top curve) in 10 d B steps. The scale at the bottom is an E R B scale, which is closely related to distance along the basilar membrane. The corresponding frequency is shown at the top. The rightpanel ( B ) shows specific loudness patterns corresponding to the excitation patterns. Over- all loudness in sones is assumed to be equal to the area under the specific loudness pattern for a given level.

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Fitting hearing aids

2 0 , , , , , , , , I I , 1

10

319

m 2 0.2

0 0.1

P

-0

0

= - ._

Q 0.05 (I)

0.02

0.01 0 10 20 30 40 50 60 70 80 90 100 110

Excitation level, dB

Fig. 2. Functions showing the transformation from excitation level to specific loudness, N, for a series of values of the excitation level at absolute threshold, L,,,@ The value of N is plotted on a log scale as a function of excitation level in decibels (also a log scale).

pattern is called a specific loudness pattern. Examples of specific loudness patterns are shown in panel B of Fig. 1. The overall loudness of a given sound, in sones, is assumed to be equal to the sum of the loudness in each ERB. This is

loss (in dB) at a given frequency into a compo- nent resulting from OHC damage and a compo- nent resulting from IHC (and neural) damage:

( 1 ) HLOHC+HLIHC=HLTOTAL equal to the total area under the specific loudness pattern plotted as N versus ERB. Thus the loudness of any sound, including a single sinusoid, is assumed to depend partly on the spreading of excitation along the BM.

Consider now the application of the model to people with cochlear hearing loss. The elevation of absolute threshold owing to cochlear hearing loss can occur in two main ways. First, damage to the outer hair cells (OHCs) impairs the operation of the ‘active mechanism’ that amplifies the BM response to weak sounds (Moore, 1995; Yates, 1995). This results in reduced BM vibration for a given low sound level. Hence, the sound level has to be increased to give a just-detectable amount of vibration. Second, inner hair cells (IHC) damage can result in reduced efficiency of transduc- tion, so the amount of BM vibration needed to reach threshold is higher than normal. In principle, it is possible to partition the overall hearing

For example, if the total hearing loss at a given frequency is 60 dB, 40 dB of that loss might be a result of OHC damage and 20 dB a consequence of IHC damage. In the model, it is assumed that HLoHc cannot be greater than 65 dB for frequencies of 2 kHz and above, and 55 dB for frequencies below that. Any loss greater than this must reflect a mixture of OHC loss and IHC loss. Hearing losses less than this may also reflect a mixture of OHC loss and IHC loss. Note that the proportion of a hearing loss that is attributed to OHC or IHC damage is not the same as the proportion of OHCs and IHCs that are damaged or lost. In the above example, 40 dB of the hearing loss was attributed to OHC damage and 20 dB to IHC damage, but this does not imply that damage to the OHCs was twice as great as damage to IHCs.

Damage to the OHCs is modelled by increasing the value of ETHRQ, which results in a steeper

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320 B. C. J. Moore and B. R. Glasberg

growth of specific loudness with increasing excitation level; see Fig. 2. This mimics the reduction in, or loss of, the compressive non-linearity in the input-output function of the BM, which is associated mainly with OHC damage (Ruggero and Rich, 1991; Moore, 1995); the perceptual consequence of this is loudness recruitment (Moore, 1995). IHC damage is modelled by an attenua- tion of the calculated excitation level at each frequency.

Frequency selectivity is usually reduced in cases of cochlear hearing loss; for a review, see Moore (1995). For a sinusoidal stimulus, this leads to an excitation pattern that is broader in an impaired ear than in a normal ear. Moore and Glasberg (1997) developed a series of equations that described empirically how the sharpness of the auditory filters varied with sound level and with hearing loss. The degree of broadening with hearing loss was assumed to depend specifically on HLOHc rather than on HI,,,,,,. Excitation patterns calculated using these equations become broader with increasing hearing loss, but

the patterns change less in shape with level as the hearing loss increases. These broader excitation patterns are used in the loudness model.

The model also allows for the possibility of complete loss of IHCs or functional neurones at certain places within the cochlea. These places are referred to as ‘dead regions’ (Moore, 1995; Moore et al., 1997b). Excitation at these places is assumed to lead to zero specific loudness.

The predictions of the model were compared with empirical data obtained using subjects with unilateral cochlear hearing loss who were required to make loudness matches between tones presented alternately to their two ears (Moore and Glasberg, 1997). The model fitted these data very well. An example of the data and of the predictions of the model is shown in Fig. 3. The predictions were also compared with data in the literature on loudness matches between narrowband and broadband sounds. In normally hearing subjects, the overall level of a broadband sound is less than that of a narrowband sound at the point of equal loudness (except at very low

100

80

-I a

9 40

60

40

20

Fig. 3. The symbols show the results of loudness matches of sinusoidal tones between the two ears for a subject with a unilateral cochlear hearing loss. Asterisks show the absolute threshold for each ear. Each panel shows results for a different signal frequency. The curves are predictions of the model described in the text. The diagonal dotted lines indicate equal levels in the two ears.

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Fitting hearing aids 321

sound levels). In people with cochlear hearing loss, the difference in level at the point of equal loudness is much smaller than normal. The model correctly predicted these effects. Analyses using the model indicated that the proportion of a hearing loss that can be attributed to OHC damage typically varies from about 50% to 100%. On average, the proportion for mild and moderate losses was about 80%.

Use of loudness models in hearing-aid fitting Loudness models can be used in a variety of ways for fitting hearing aids. One approach is to attempt to restore loudness perception to ‘normal’ by means of multi-band, fast-acting compression; the loudness model is used to calculate the required gain in each band on a moment-by- moment basis, over timescales of 10-50 ms (Kollmeier and Hohmann, 1995).

A different approach is to apply frequency selective amplification so as to make the loudness of speech equal (as far as possible) in different frequency bands. This approach has been used especially for the fitting of linear hearing aids. The basic idea here is to place as much of the speech spectrum as possible above absolute threshold for a given overall loudness. This idea lies behind the NAL(R) formula for prescribing the gain of a linear hearing aid as a function of frequency (Byrne and Dillon, 1986). This prescription aims to amplify all frequency bands of speech to an equal, comfortable loudness, for speech at normal conversational levels (65-70 dB SPL). In principle, the frequency- selective gain should result in a specific loudness pattern that is flat (constant specific loudness) over the frequency range that is most important for speech, namely 500 to 4000 Hz.

The goal of the NAL procedure seems emi- nently reasonable. Making each frequency band in speech equally loud can ensure that no single band contributes excessively to loudness. Thus the overall amplification can be increased, increasing the proportion of the speech spectrum that is audible while maintaining a comfortable loudness. However, as will be illustrated later, application of the Cambridge loudness model indicates that, in fact, the NAL prescription does not meet its stated goal of amplifying all bands of speech to an equal comfortable loudness. This paper describes a new prescription rule, the ‘Cambridge formula’, that comes closer to meet- ing this goal. The excitation patterns and specific

loudness patterns resulting from application of the new rule are compared with those obtained using the NAL formula, and also using two other fitting rationales: one, called FIG6, is based on restoring loudness to ‘normal’ (Killion and Fikret-Pasa, 1993); the other, called the Desired Sensation Level (DSL) method (Seewald, 1992), aims to amplify speech of moderate level so that as much as possible of the speech spectrum is above threshold. It should be emphasized that these are only a few among many possible procedures; see, for example, Humes (1991). However, these three procedures are rather widely used, and can be considered representative of the available threshold-based prescription rules.

To help determine which, if any, of these methods is ‘best’, the loudness model was extended to allow calculation of a form of the articulation index (AI) (Pavlovic, 1987), which gives an esti- mate of the proportion of the speech spectrum that is audible. We used this method to compare AIs for speech amplified according to the Cam- bridge formula, NAL, FIG6 and DSL under conditions where the overall gains were adjusted to give a fixed comfortable loudness.

Approaches similar to this have been described previously by Leijon (1989; 1990) and by Studebaker (1992). For example, Studebaker used a loudness model and a calculation of the weighted audibility index (WAI) to address the following question: ‘was weighted audibility greater before or after the frequency-gain response adjustment assuming that gain was reset to achieve the same loudness in each case’. He described this approach as ‘cost-benefit analysis’. Our approach differs from those of Lei- jon and Studebaker in two main ways. First, they did not use their loudness models to calculate the frequency-gain characteristic needed to produce a flat specific loudness pattern. Instead, the models were used to calculate the overall gain adjustment necessary to equate overall loudness for different frequency-gain characteristics. Second, the loudness models used by them were not as well validated as the model used here, as least in terms of their application to hearing impairment.

Development of the Cambridge formula The Cambridge formula was developed by con- sidering a large number of hypothetical hearing losses, including flat losses of varying severity, losses increasing at high frequency and losses increasing at low frequency. It was assumed in all

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cases that the proportion of the hearing loss attributable to OHC damage had the typical value of 80%, with the restriction that the loss resulting from OHC damage could not exceed 55 dB (Moore and Glasberg, 1997). The effect of having other degrees of OHC damage is considered later in this paper.

The basic input to the model was the spectrum of speech with an overall level of 65 dB SPL. The spectral shape was the same as the long-term average value published by Byrne et al. (1994). When the model was set up to simulate normal hearing, using binaural listening in free field (frontal incidence), the resulting calculated loudness was 23.1 sones. For each of the hypothetical hearing losses, a frequency-dependent gain was applied to the 65 dB speech before application to the model. The gain was specified at each audiometric frequency (including 750,1500,3000 and 5000 Hz), and linear interpolation was used to calculate gains between audiometric frequencies. The model was set up to simulate the hearing loss, and the gain was adjusted at each frequency to achieve two goals: the overall loudness should be 23.1 sones (for binaural listening) and the specific loudness pattern should be as flat as possible over the range 500 to 4000 Hz. The resulting gains are the insertion gains (IG) required to achieve the goal of a flat specific loudness pattern and a comfortable overall loudness (the same loudness as experienced by a normally hearing person listening to speech at 65 dB SPL using two ears).

It was found that these two goals could be met with good accuracy using a simple formula. Applying this formula to losses ranging from mild to severe, the specific loudness in the frequency range 500 to 4000 Hz was never less than 0.75 or greater than 1.19. The overall calculated loudness was never less than 21 sones or more than 26 sones. In the formula, the IG at a given frequency is linearly related to the hearing loss at that frequency. Also, the slopes of the functions relating IG to hearing loss do not vary with

frequency; only a frequency-dependent intercept is required. The formula is:

IG = HL x 0.48 + INT, (2)

where HL stands for the absolute threshold in dB HL and INT is a frequency-dependent intercept. The value of INT is given in Table 1 for each frequency. Above 5 kHz, gains are limited to the value at 5 kHz.

The goal of achieving a flat specific loudness pattern was restricted to the frequency range 500 to 4000 Hz, since that is the frequency range that is most important for speech intelligibility (see below for more details). Below 500 Hz, we decided to reduce the gains below those required to achieve a flat specific loudness pattern. This was done to reduce masking of the speech by low- frequency environmental sounds, such as car noise and noise from ventilation and air-condi- tioning systems. These sounds have considerable energy at low frequencies which can have a masking effect on the medium and high frequencies in speech. Also, when several people are talking in a typical room, the higher frequencies in the speech are absorbed by room reflections much more than the low frequencies. The reverberant sound field therefore contains predominantly low frequencies, which again can have a masking effect on higher frequencies. Such masking may be especially important for people with cochlear hearing loss, since they suffer more than normally hearing people from the ‘upward spread of masking’ (Glasberg and Moore, 1986). The intercept values at 125 and 250 Hz were chosen so as to reduce upward spread of masking while avoiding making the speech quality too ‘tinny’. Pilot exper- iments with hearing-impaired subjects were undertaken to establish intercept values that gave acceptable speech quality. In theory, the intercept values at low frequencies could lead to negative gains for mild hearing losses. In practice, where gains would be negative, they are set to zero.

Table 1. Values of the intercept (INT) in the Cambridge formula for each audiometric frequency ( M z )

Frequency 0.125 0.25 0.5 0.75 1.0 1.5 2.0 3.0 4.0 5.0

INT -11 -10 -8 -6 0 -1 1 -1 0 1

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binaural listening and that 80% of the hearing loss was attributable to OHC damage). The spectral shape of the speech was as described in Byrne et al. (1994). The calculation took into account the transformation from free field to eardrum assuming frontal incidence (Shaw, 1974). The lower of the two solid lines shows the excitation

Comparison of excitation patterns and specific loudness patterns We start by comparing excitation patterns and specific loudness patterns for a normal ear and a hypothetical impaired ear with a sloping hearing loss (flat below 500 Hz; for the audiometric thresholds, see table 3 below). In the remaining

80

70

figures of this paper, excitation patterns and specific loudness patterns will be plotted on a logarithmic frequency scale rather than an ERB scale, since the former is more familiar. Also, the use of a frequency scale allows more ready identi- fication of the regions of the curves that are most relevant to speech perception (500 to 40000 Hz). However, the shapes of excitation patterns and specific loudness patterns are similar on an ERB scale and on a logarithmic frequency scale for centre frequencies above 500 Hz.

Figure 4 shows excitation patterns for speech with an overall level of 65 dB SPL, calculated using the Cambridge loudness model (assuming

- Sloping loss Cambridge

/-..

NAL ,,;,>\ y)’ - 3

- /. ‘..

‘..0‘. ..-.. -

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required for threshold in a normal ear, and the lower dashed line shows the excitation required for threshold for the hypothetical ear with a sloping hearing loss. The upper of the two solid lines shows the excitation pattern evoked by the speech in a normal ear. It lies well above the threshold excitation over the whole frequency range from about 100 Hz to 10 kHz. The upper long-dashed line shows the excitation evoked by the speech in the impaired ear when NAL selective amplification was applied. The dotted line shows the excitation evoked by the speech in the impaired ear when FIG6 selective amplification was applied. The gains used here were those

90 , I I I I I I I , , I I I , , , , , ,

Fig, 4. Excitation patterns for speech with an overall level of 65 d B SPL, calculated using the Cam- bridge loudness model. The lower solid line shows the excitation required for threshold in a normal ear, and the lower dashed line shows the excitation required for threshold for a hypothetical ear with a sloping hearing loss; see Table 3 for the audiometric thresholds. The upper solid line shows the excitation pattern evoked in a normal ear. The upper long-dashed line shows the excitation evoked in the impaired ear when NAL gains were applied. The dotted line shows the excitation evoked in the impaired ear when FIG6 gains were applied. The dashed-dotted line shows the excitation evoked in the impaired ear when gains prescribed by the Cambridge formula were applied.

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324 B. C. J. Moore and B. R. Glasberg

appropriate for a 65 dB input; the FIG6-prescribed gains are actually level dependent. The dashed-dotted line shows the excitation evoked by the speech in the impaired ear when selective amplification was applied according to the Cam- bridge formula.

Figure 5 shows specific loudness patterns corresponding to the excitation patterns shown in Fig. 4. Although the NAL procedure aims to produce equal loudness across frequency, the specific loudness pattern with NAL amplification (dashed line) is not, in fact, flat; the specific loudness drops markedly above about 1.6 kHz. For FIG6 amplification (dotted line), the specific loudness is greater below 1 kHz than above it. Amplification according to the Cambridge formula (dashed-dotted line) gives a reasonably flat loudness pattern over the range 500 to 4000 Hz.

Figures 6 and 7 show a similar comparison for the Cambridge formula and DSL, for the same hypothetical hearing loss. The DSL method can be applied both to linear hearing aids and to aids with compression (Cornelisse et al., 1995). How- ever, here we consider only the application of the method to fitting of a linear hearing aid. The method aims to amplify mid-level speech so that the entire speech spectrum is above threshold (at least for mild to moderate losses). Generally, this

method calls for greater gains than the Cambridge formula, especially at high frequencies. For the sloping loss illustrated in Figs 6 and 7, and in Table 3, the DSL method prescribes gains of 36 and 48 dB at 4 and 6 kHz, respectively, compared with gains of 29 and 33 dB prescribed by the Cam- bridge formula. It is debatable whether such high gains could be achieved in practice, as the gains at high frequencies are usually limited by acoustic feedback. In any case, such high gains would probably lead to unacceptable loudness and tone quality. The calculated loudness for the 65 dB speech amplified according to the DSL method was 42.5 sones, almost double the loudness of 23.1 sones calculated for the Cambridge formula. Furthermore, the specific loudness was greatest in the range 3.3 to 5.3 kHz, which would probably be associated with a very shrill tone quality. In practice, a hearing-aid user would probably reduce the overall gain prescribed by the DSL method to achieve a comfortable loudness. This point is discussed in more detail later on.

Figures 8 and 9 show excitation patterns and specific loudness patterns for a hypothetical flat loss of 50 dB at all frequencies. Again, the specific loudness pattern with NAL amplification (dashed line) drops markedly above about 1.6 kHz. For FIG6 amplification (dotted line),

2.0

1.8

1.6

1.4 m . g 1.2

2 1.0 6

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0.8

6 0.6

0.4

0.2

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I I I I I I , , I I I I I 4 I I

Sloping loss

I I I I 1 1 1 1 1 1 ' I I I I I I I I I I

0.05 0.1 0.2 0.5 1 2 5 10 Frequency, kHz

Fig. 5. Specific loudnesspatterns corresponding to the excitation patterns in Fig. 4.

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90

80

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60 m u

t I Sloping loss

I I I I , , , , I I I I , , , , .... ,.-. ...

20

10

0 0.05 0.1 0.2 0.5 1 2 5 10

Frequency, kHz

Fig. 6. As Fig. 4, but comparing excitations patterns using Cambridge-prescribed gains and DSL- prescribed gains.

2.0 t I I I I I I I , , I I I I I I , , ,

1.8

1.6

1.4

1.2

1 .o

0.8

0.6

0.4

0.2

0 0.05 0.1 0.2 0.5 1 2 5 10

Frequency, kHz

Fig. 7. Specific loudness patterns corresponding to the excitation patterns in Fig. 6.

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326

the specific loudness pattern shows a large peak around 500 Hz. The Cambridge formula gives flatter specific loudness functions than the NAL or FIG6 prescriptions.

B.C.J. Moore and B.R. Glasberg

Figures 10 and 11 make a similar comparison between the Cambridge formula and the DSL method, for the hypothetical flat loss. As before, the DSL method prescribed higher gains than the

90 I I r , I , , I , 8 1 I I I I , ,

Flat loss

l o 0 L-L-L-d Normal threshold

0.05 0.1 0.2 0.5 1 2 5 10 Frequency, kHz

Fig. 8. As Fig. 4, but for a hypothetical ear with aflat hearing loss of 50 dB.

2.0

1.8

1.6

m [r 1.4 Y 6 1.2 al

m 6 8 1.0 U

0.8

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0.05 0.1 0.2 0.5 1 2 5 10 Frequency, kHz

Fig. 9. Specific loudness patterns corresponding to the excitation patterns in Fig. 8.

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I I 8 I I , I , , I I I I I , , , I 0.05 0.1 0.2 0.5 1 2 5 10

Frequency, kHz

Fig. 10. As Fig. 8, but comparing excitations patterns using Cambridge-prescribed gains and DSL- prescribed gains.

2.0

1.8

1.6

m a: 1.4 P

s 1.2 a,

In- 2 1.0 U

0.8

2 0.6

0.4

0.2

0 0.'

._ c

Fig. 11. Specific loudnesspatterns corresponding to the excitation patterns in Fig. 10.

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Cambridge formula. The specific loudness pattern with amplification according to the DSL method shows a large peak around 500 Hz. The overall calculated loudness was 43.6 sones, again markedly greater than the overall loudness produced by application of the Cambridge formula.

Work with other patterns of hearing loss generally revealed similar patterns to those described above: application of the Cambridge formula led to a calculated loudness that was close to the normal value for 65 dB speech (23.1 sones) for losses up to 70 dB HL; the range was 21 to 26 sones. Similarly, the Cambridge formula always gave a reasonably flat specific loudness pattern; the range of specific loudness for the frequency range 500 to 4000 Hz was 0.75 to 1.19. Applica- tion of the NAL formula generally led to slightly lower overall loudness, and did not give flat specific loudness patterns; there was too much gain at mid frequencies and too little gain at high frequencies. The FIG6 gains generally led to an overall loudness that was slightly lower than normal, and gave specific loudness patterns with large peaks at low frequencies. The DSL gains led to high overall calculated loudness, and to specific loudness patterns that were not flat; the positions of the peaks depended on the configu- ration of the hearing loss.

To help assess the merits of these different approaches to amplification, we developed a method of calculating a form of the articulation index from the excitation patterns produced by the loudness model. Using this, we could address the question: for a fixed overall loudness, which method of prescribing the frequency-gain characteristic leads to the highest AI? As described earlier, a similar question has been addressed by Leijon (1989; 1990) and by Studebaker (1992).

Development of a measure of the A1 We have developed a procedure for calculating a form of the A1 (French and Steinberg, 1947;

Pavlovic, 1987) from the excitation pattern. The excitation pattern is plotted on an ERB scale, the same as that used in the loudness model (Glas- berg and Moore, 1990). For points with equal ERB spacing along the frequency scale, we calculate the amount by which the excitation level exceeds the excitation required for threshold. From this we calculate the proportion of the speech dynamic range that is above threshold in that frequency band, assuming that this range extends from 18 dB below the rms level to 12 dB above it.’ For example, if the rms excitation is 18 dB above threshold, then the proportion is 1, whereas if the rms excitation is at threshold, the proportion is 12/30 = 0.4. Band importance functions are adapted from those for average speech as specified in the ‘critical band SII procedure’ (American National Standard Methods for the Calculation of the Speech Intelligibility Index, draft V4.1,1996). Values have been adjusted to allow for the difference between traditional critical bandwidth values (Zwicker and Terhardt, 1980) and ERE3 values (Glasberg and Moore, 1990). The importance values are specified in Table 2.

We calculate the A1 by multiplying the proportion of the speech dynamic range that is above threshold in a given band, by the importance value for that band, and then summing across all bands from 189.7 Hz to 9.302 kHz.

This approach may be over-simplified, as the importance value for a given frequency band might be affected by the degree of hearing loss at the frequency corresponding to that band (Pavlovic et al., 1986). For example, a large hearing loss at high frequencies might lead to less effective use of high-frequency information in speech, even when that information is made audible by amplification. However, extended experi- ence with amplification can lead to improvements in the use of information from frequency regions that were previously inaudible (Gatehouse, 1992). Therefore, it is not clear

I Our calculation of the A1 is based on the assumption that the audibility of excitation at a particular centre frequency is closely related to the audibility of the speech spectrum at that frequency. In other words, we are assuming that the excitation at a specific frequency is determined by the speech energy close to that frequency, rather than the spread of excitation from adjacent frequencies. This assumption is not always valid. When it is not valid, the AI calculated by our procedure will be an overestimate of the ‘true’ AI. When the excitation pattern is reasonably flat, and in particular does not have any regions with a steep downward slope, then our assumption is probably not strongly violated; the excitation at a particular centre frequency will be determined largely by the speech energy around that frequency. However, when the excitation pattern has distinct peaks and dips, the excitation in the dips may arise from spread of excitation and the A1 will then be overestimated. We conclude that overestimation of the A1 is less when the excitation pattern is smooth than when it has peaks and dips. Since the Cambridge formula leads to smoother excitation patterns than the other methods considered, the A1 is likely to have been overestimated by a smaller amount for the Cambridge formula than for the other methods.

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Table 2. Values of the importance function for frequencies with 1-ERB spacing. These importance values are used in the calculation of the articulation index (AI); see text for details

Frequency lrHz

0.1897 0.2373 0.2904 0.3495 0.4153 0.4886 0.5702 0.6612 0.7625 0.8753 1.0009 1.1409 1.2968 1.4704 1.6638 1.8791 2.1190 2.3862 2.6838 3.0152 3.3844 3.7956 4.2535 4.7636 5.3317 5.9645 6.6692 7.4542 8.3285 9.3023

Importance

0.0036 0.0076 0.0130 0.0202 0.0270 0.0360 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0450 0.0405 0.0360 0.0292 0.0225 0.0180 0.0135 0.0090 0.0045

whether the calculation of the A1 should be mod- ified to give reduced importance values to frequency bands falling in a region of large hearing loss. For the moment, we continue to use the importance functions derived using subjects with normal hearing.

Calculations of the A1 for a fixed overall loudness We return now to the question posed earlier: for a fixed overall loudness, which method of prescribing the frequency-gain characteristic leads to the highest AI? To address this question, we

first calculated the overall loudness of 65 dB speech for the hypothetical hearing losses described earlier, after application of the frequency-gain characteristic prescribed by each approach. If the overall loudness in a given case was different from 23.1 sones, the overall gains were adjusted upwards or downwards to achieve an overall loudness as close as possible to 23.1 sones. This adjustment was intended to be comparable to what could be achieved by adjustment of the volume controls on hearing aids; if speech is too loud, the user will sim- ply reduce all gains using the volume control. Of course it is possible that, with very different frequency response shapes, the user of a hearing aid would not adjust the volume control to achieve a fixed overall loudness. However, the choice of a fixed comfortable loudness as the criterion seems reasonable, and a similar criterion has been adopted by others (Studebaker, 1992). Thevalue of the A1 was calculated both for the original gain values and for the adjusted gains.

Table 3 illustrates the outcome of such calculations for the sloping loss used for Figs 4 to 7. The first row shows the absolute thresholds in dB HL. The second row shows the NAL-prescribed insertion gains. The two numbers at the right of the row indicate the calculated A1 and the calculated overall loudness in sones. The A1 is less than 1, indicat- ing that part of the speech spectrum for speech at 65 dB SPL would be inaudible. The overall loudness of 18.4 sones is somewhat less than the loudness of about 23.1 sones that would occur for a normally hearing person without amplification. The third row shows the effect of increasing all of the NAL gains by 2.5 dB. This increases the overall loudness to its normal value, and increases the A1 from 0.84 to 0.89. Rows 4 and 5 of the table show similar calculations for the FIG6 procedure. Again, the original loudness is slightly low. Increasing all gains by 3.6 dB gives normal loudness and increases the A1 from 0.81 to 0.89. Rows 6 and 7 show results for the DSL method. The prescribed gains lead to a high overall loudness and a high A1 of 0.99; the high A1 is expected, as the procedure aims to place most of the speech spectrum above absolute threshold. A gain reduction of 6.5 dB is required to give a loudness of 23.1 sones. With this reduced gain, the A1 drops to 0.91. The final row shows the outcome using the Cambridge formula. This gives the appropriate overall loudness without any adjustment of gain. For the fixed overall loudness of 23.1 sones, the Cambridge procedure gives the highest A1 of 0.93.

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Table 3. The two right-most columns show A1 and loudness values (in sones) for speech with a 65 dB SPL input level subjected to amplification according to NAL, FIG6, DSL or the Cambridge formula; the assumed hearing loss in dB is shown in the first row of the table. For each formula, the A1 and loudness values are given both with the original insertion gain (IG) values (in dB), and with all gains adjusted (as could be done with a volume control) so as to achieve a comfortable overall loudness of 23 sones. The adjusted values are shown in italics

Frequency, kHz 0.125 0.25 0.5 0.75 1.0 1.5 2.0 3.0 4.0 5.0 6.0 A1 Loudness

HL

NAL + 2.5

FIG6+3.6

IG-NAL

IG-FIG6

IG-DSL DSL - 6.5 IG-Camb

30 30 30 35 40 45 50 55 60 65 70 0 0 7 14 19 21 21 21 23 26 0.84 18.4

0.89 23.0 6 6 6 12 15 18 21 24 24 0.81 16.6

0.89 23.1 13 13 20 26 36 48 0.99 42.8

0.91 23.1 3 4 6 11 19 21 25 25 29 33 33 0.93 23.1

Table 4. As Table 3, but for a flat hearing loss of 50 dB

Frequency, kHz 0.125 0.25 0.5 0.75 1.0 1.5

HL 50 50 50 50 50 50

NAL + 1 IG-FIG6 18 18 18 18 18 FIG6 + 0.8 IG-DSL 23 23 26 25

IG-Camb 13 14 16 18 24 23 Camb - 1.2

IG-NAL 6 6 15 20 24 24

DSL - 6.9

Table 4 gives a further example, for the hypothetical flat loss discussed earlier. To achieve the normal loudness of 23.1 sones, the overall gains had to be adjusted by +1, +0.8, -6.9 and -1.2 dB for the NAL, FIG6, DSL and Cambridge methods, respectively. The Cambridge procedure again gave the highest A1 of all the procedures for a fixed overall loudness of 23.1 sones.

We will consider briefly two further examples, concentrating mainly on the comparison of the NAL formula and the Cambridge formula. The first example is of a case with near-normal thresholds (16 dB HL) up to 1 kHz, with a loss increasing steeply to 80 dB at 6 kHz. The NAL formula led to a calculated overall loudness of 16.8 sones and a specific loudness that varied from 1.045 at 660 Hz to 0.14 at 3800 Hz; the

2.0 3.0 4.0 5.0 6.0 A1 Loudness

50 50 50 50 50 22 21 21 21 0.92 21.0

0.94 23.0 18 18 18 18 0.86 21.3

0.88 23.0 26 29 29 33 1.0 43.6

0.92 23.1 25 23 24 25 25 0.97 26.0

0.95 23.0

specific loudness was zero for higher frequencies. Increasing all gains by 4 dB led to a calculated loudness of 23.1 sones, but the specific loudness still varied considerably across frequency, from 1.32 at 660 Hz to 0.3 at 4000 Hz. The calculated A1 in this case was 0.82. The Cambridge formula led to a calculated overall loudness of 21.2 sones and a specific loudness that varied from 0.78 at 760 Hz to 1.06 at 3400 Hz. The calculated A1 was 0.88.

The second additional example is of a reverse slope audiogram. The thresholds were taken to be 65 dB HL for frequencies up to 500 Hz, 50 dB HL at 1000 Hz, 40 dB at 2000 Hz and 30 dB for frequencies of 4000 Hz and above. The NAL formula led to a calculated overall loudness of 22.1 sones and a specific loudness that varied

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Fitting hearing aids 33 1

from 1.35 at 880 Hz to 0.88 at 4000 Hz. The calculated A1 was 0.92. The Cambridge formula led to a calculated overall loudness of 24.4 sones and a specific loudness that varied from 1.32 at 660 Hz to 0.85 at 4000 Hz. The calculated A1 was 0.95. In this case, the difference between the two formulae was small.

The examples presented in Tables 3 and 4, together with the two additional examples discussed above, are representative of what was found with other hypothetical hearing losses varying in severity and slope, including flat losses up to 70dB HL. However, we have not attempted to evaluate cases where the overall loss was in the severe-to-profound range, as the loudness model has not been validated for such losses. Generally, for mild to severe losses, the Cambridge formula led to an overall loudness that was close to the target value of 23.1 sones. It was never necessary to adjust all gains by more than 1.5 dB to achieve the target loudness. Fur- thermore, the specific loudness patterns were generally rather flat over the frequency range 500 to 4000 Hz. The NAL and FIG6 formulae often, but not always, led to an overall loudness lower than the target value. Specific loudness patterns often had mid-frequency peaks for the NAL formula, and low-frequency peaks for FIG6. The DSL method almost always led to an overall loudness that was too great, and the specific loudness patterns often showed distinct peaks, although the positions of these depended on the hearing loss.

Discussion Although the rationale behind the Cambridge formula is similar to that behind the NAL formula, the two differ nevertheless. Part of the dis- crepancy may arise from the fact that the long-term average spectrum assumed in develop- ing the NAL formula differs from that used by us. We used a spectrum derived on the basis of a large multi-centre study using different lan- guages (Byrne et al., 1994). This spectrum can be considered as highly representative, although, of course, the spectra of individual speakers can vary markedly from the average.

At first sight, our conclusion that the Cam- bridge formula is preferable to the NAL formula might appear to be inconsistent with data in the literature. For example, Byrne and Cotton (1988) compared aids fitted according to the NAL formula with systematic variations from that

formula. In two conditions, the slope of the response above 1250 Hz was increased or decreased by 6 dB/oct. In another two conditions, the slope of the response below 1250 Hz was increased or decreased by 6 dB/oct. The NAL response was generally preferred over the variations both for judged intelligibility and for pleas- antness. However, none of the response variations would have led to frequency responses close to those prescribed by the Cambridge formula. For example, increasing the slope above 1250 Hz by 6 dB/oct would have led to more high- frequency gain than prescribed by the Cambridge formula. Decreasing the slope below 1250 Hz by 6 dB/oct would have led to much less low-frequency gain than prescribed by the Cambridge formula. Thus, this experiment did not include any conditions that would allow a choice between the Cambridge formula and the NAL formula.

Studebaker (1992) also assessed the effect of frequency response variations relative to the basic response prescribed by the NAL formula. He calculated a weighted audibility index (WAI) for each frequency response, using a loudness model to adjust overall gains so as to achieve a fixed calculated loudness. He found that the highest WAI was obtained for a response close to the NAL response. Again, however, the frequency-response manipulations used by Stude- baker did not include any responses that would have been a close approximation to the response prescribed by the Cambridge formula. Also, as noted earlier, the loudness model used by Stude- baker has not been validated in its application to hearing impairment.

It should be emphasized that the Cambridge loudness model has been evaluated mainly for hearing losses ranging up to about 80 dB, and it may well not be valid for profound losses. Corre- spondingly, the calculations described in this paper were restricted to hearing losses up to 80 dB. Therefore, the Cambridge formula may well not be applicable in cases of severe to profound hearing loss.

Whether or not the formula achieves its goals on average, some fine tuning is likely to be needed to suit the preferences of the individual user and to allow for the fact that the proportion of the hearing loss attributable to OHC damage will vary from one hearing-impaired person to another; recall that the excitation patterns and specific loudness patterns in Figs 4-11 were calculated assuming that 80% of the hearing loss

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was attributable to OHC damage. To assess the likely influence of individual differences in OHC damage, the calculations of loudness with application of the Cambridge formula were repeated assuming different degrees of OHC damage. The previous assumption that 80% of the hearing loss was attributable to OHC damage may be considered as representing a typical hearing loss (Moore and Glasberg, 1997). However, the range may vary from 100% to 50% in individual cases (Moore and Glasberg, 1997).

Consider, as an example, the sloping hearing loss shown in Figs 4-7, and in Table 3. When 80% of the hearing loss was attributed to OHC damage, the calculated loudness with amplification according to the Cambridge formula was 23.1 sones. When all of the hearing loss (up to a maximum of 55 dB) was assumed to be attributable to OHC loss, the calculated loudness increased to 35.7 sones. The specific loudness varied from 1.36 to 1.71 (a factor of 1.26) over the range 500 to 4000 Hz. To restore loudness to the value of 23.1 sones, all gains had to be reduced by 4.8 dB. Once this was done, the specific loudness pattern became somewhat flatter; the specific loudness varied from 0.97 to 1.15 (a factor of 1.19) over the range 500 Hz to 4000 Hz.

When 50% of the hearing loss was assumed to be attributable to OHC loss, the calculated loudness decreased to 10.8 sones. The specific loudness varied from 0.34 to 0.62 (a factor of 1.82) over the range 500 to 4000 Hz. In this case, all gains needed to be increased by 9.3 dB to restore the loudness to 23.1 sones. When this was done, the specific loudness pattern was again reasonably flat, the specific loudness varying from 0.79 to 1.13 (a factor of 1.43) over the range 500 to 4000 Hz. Thus, for these two cases, simple adjustment of the volume control would be sufficient to restore a comfortable loudness and a reasonably flat specific loudness pattern.

A more problematic situation is when the proportion of OHC loss varies with frequency. In such a case, the specific loudness pattern produced by application of the Cambridge formula would be less flat. To illustrate this, we considered two extreme forms of the hearing loss specified in Table 3. In one, the value of HL,,, was assumed to be 50% of H h O T A L for frequencies up to 1 kHz, and 100% of H b O T A L (up to a maximum of 55 dB) for frequencies of 2 kHz and above (with linear interpolation in between). Application of the Cambridge formula gave a

calculated loudness of 24.1 sones, not far from the ‘target’ value. However, the specific loudness varied from about 0.46 at 1000 Hz to 1.71 at 2100 Hz. In the other extreme form, the value of HL,,, was assumed to be 100% of H b O T A L for frequencies up to 1 kHz, and 50% of HLTOTAL for frequencies of 2 kHz and above (with linear interpolation in between). Application of the Cambridge formula gave a calculated loudness of 21.1 sones, again not far from the ‘target’ value. However, specific loudness varied from about 1.39 at 600 Hz to 0.34 at 3000 Hz. Clearly, in these extreme cases, adjustment of the frequency response shape would be needed to achieve a flat specific loudness pattern. Nevertheless, it appears that, for most cases, the Cambridge formula would lead to a reasonably flat specific loudness pattern, after appropriate adjustment of the volume control.

Coincidentally, the Cambridge formula leads to similar recommended insertion gains to the POGO rule described by McCandless and Lyre- gard (1983); usually, the recommended gains do not differ by more than 3 dB for the Cambridge and POGO formulas, although sometimes the deviation reaches 4 or 5 dB. However, the Cam- bridge formula generally does lead to somewhat flatter specific loudness patterns than the POGO formula. For example, for the loss specified in Table 3 (assuming that 80% of the hearing loss was a result of OHC damage, up to a maximum of 55 dB), the calculated overall loudness using gains according to the POGO formula was 25.8 sones; the specific loudness varied from 0.99 to 1.26 (a factor of 1.27) over the range 500 to 4000 Hz. For the same loss, the Cambridge formula led to an overall loudness of 23.1 sones and a range of specific loudness from 0.88 to 1.05 (a factor of 1.19). For the loss specified in Table 4 (assuming that 80% of the hearing loss was due to OHC damage), the calculated overall loudness using gains according to the POGO formula was 30.1 sones; the specific loudness varied from 0.98 to 1.61 (a factor of 1.64) over the range 500 to 4000 Hz. For the same loss, the Cambridge formula led to an overall loudness of 26.0 sones and a range of specific loudness from 0.97 to 1.19 (a factor of 1.23).

One might argue that the differences described above are too small to be of significance in clini- cal practice; the errors in fitting are likely to be larger than the differences between the formulae. However, it would seem desirable to specify the

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target response as accurately as possible, to avoid cumulative errors. As the Cambridge formula leads to flatter specific loudness patterns than POGO, and leads to an overall loudness that is more nearly constant, we believe that the Cam- bridge formula is preferable. Also, it is likely that future generations of digital hearing aids will allow very precise adjustment of frequency response, and in this case it is desirable to have a fitting formula with a firm theoretical basis.

We believe that the Cambridge formula should be suitable for fitting linear hearing aids. It should also be suitable for fitting hearing aids incorporating slow-acting automatic gain control, such as the dual front-end AGC system developed at Cambridge (Moore and Glasberg, 1988; Moore et al., 1991; Moore, 1993). This system delivers speech at a comfortable overall loudness for a wide range of input levels. The Cambridge formula can be used to determine the appropriate frequency response shaping to be used in conjunction with the AGC system.

In preliminary work evaluating the Cambridge formula, we have made used of experimental digital hearing aids called ‘Audallions’, manufac- tured by Audiologic. These allow very precise frequency response shaping. In collaboration with Drs Michael Stone and Joseph Alcantara, we have been evaluating the use of the Cam- bridge formula for fitting Audallions pro- grammed to implement the dual-front end AGC system. After initial fitting according to the Cam- bridge formula, an adaptive procedure is used to fine-tune the frequency-response shape; this procedure is similar to that described in Moore et al. (1998). The overall gain is adjusted so that speech with an input level of 85 dB SPL is presented at the ‘highest comfortable level’; because of the AGC system, the output level never exceeds this level. Then, the balance between the high and low frequencies is adjusted so that speech at 85 dB SPL is judged to have an acceptable tonal quality (neither too tinny nor too boomy).

Two forms of the dual front-end AGC system have been tested. One is similar to the published version, and has a high compression ratio (30). The other has a lower compression ratio of 3, intended to give some impression of changes in level in the environment while still substantially restricting the range of output sound levels. For the high compression ratio system, both ears of seven hearing-impaired subjects have been tested so far (14 ears). There were seven cases

where no change in frequency response shape was made as a result of the fine-tuning. In two cases, the relative gain at high and low frequencies was altered by less than 2 dB. In the worst case, the gain at high frequencies was reduced by 6 dB relative to that at low frequencies. For the low compression ratio system, both ears of eight hearing-impaired subjects have been tested so far (16 ears). In all 16 cases, no change in frequency response shape was made as a result of the fine tuning.

These results indicate that the Cambridge formula leads to a good tonal quality for most hearing-impaired persons, for speech presented at or below the highest comfortable level. The Cam- bridge formula clearly needs further experimental evaluation, but these preliminary results are encouraging.

Acknowledgments This work was supported by the Medical Research Council, and the European Union (SPACE project). Some of the preliminary eval- uations using the Audallion were conducted in the laboratory of Robert Peters in North Car- olina. We thank Audiologic for providing the Audallion hearing aids. Michael Stone and three anonymous reviewers provided very helpful comments on earlier versions of this paper.

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use of a loudness model for hearing-aid fitting. i. linear hearing aids

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