mechanical filtering of sound in the inner ear

Mechanical Filtering of Sound in the Inner EarAuthor(s): A. M. Brown, S. A. Gaskill and D. M. WilliamsSource: Proceedings: Biological Sciences, Vol. 250, No. 1327 (Oct. 22, 1992), pp. 29-34Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/49575 .

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Mechanical filtering of sound in the inner ear

A. M. BROWN, S. A. GASKILL AND D. M. WILLIAMS

Laboratory of Experimental Psychology, University of Sussex, Brighton, U.K.

SUMMARY

We have studied the distortion generated by the cochlea to gain insight into the mechanisms responsible for the sharp tuning or 'frequency selectivity' of the inner ear. We used two stimulating tones of moderate

intensity which are progressively separated in frequency, and measured the ear canal cubic distortion

components which are generated as a consequence of the stimulus interaction in the cochlea. We inferred that the distortion is generated from the frequency region of the higher of the two stimulus tones and that it is then band-pass filtered by a structure which is tuned to a frequency just over half an octave below that of the high-frequency tone. We suggest that the structure responsible for this band-pass filtering is the tectorial membrane, and we conclude that our results support theories of cochlear mechanics in which resonances due to the tectorial membrane interact with those of the basilar membrane to enhance the

frequency selectivity of the inner ear.

1. INTRODUCTION

The basilar membrane (BM) which supports the sensory cells in the mammalian cochlea is tuned to progressively lower frequencies from base to apex. Tones

stimulating the cochlea initiate a 'travelling wave' of vibration which reaches a maximum at the appropriate place along the BM but diminishes rapidly beyond this

point. There is a sharp peak in the mechanical response of the BM (Rhode 1971; Robles et al. 1986) which is

thought to depend on active amplification of BM

vibration by the outer hair cells in the cochlea (Neely & Kim 1983). If two tones are used to stimulate the

ear, the travelling waves of both the lower frequency tone (fl) and the higher frequency tone (f2) stimulate the f2 frequency region. Distortion is generated as a result of the interaction of the two stimuli through nonlinear processes in this region of overlap (see figure 1). The distortion is re-emitted from the ear and can be measured with a microphone in the ear canal

(Kemp 1979; Kim et al. 1980). This intermodulation distortion is so-called because its frequency depends on the frequencies of both of the stimuli rather than only one stimulus, as in the case of harmonic distortion.

If the distortion is measured while the stimuli are moved progressively apart in frequency, it has been found that the intermodulation distortion due to a cubic nonlinearity (cubic difference tones [n+ 1] fl- nf2) can only be heard by a listener or measured in the ear canal over a narrow range of stimulus frequency separation (see, for example, Goldstein 1967; Smooren-

burg 1972; Wilson 1980; Fahey & Allen 1985; Harris et al. 1989; Gaskill & Brown 1990). The nonlinear

products of this two tone interaction can therefore be used to infer some aspects of mechanical frequency selectivity or 'tuning' in the cochlea, as the distortion is giving an indication of the extent to which tones at

Proc. R. Soc. Lond. B (1992) 250, 29-34 29 Printed in Great Britain

other frequencies affect vibration at the frequency characteristic of a particular region of the cochlear

partition. When intermodulation distortion is generated, the generation site is clearly being influenced by more than one stimulus.

In a previous comparative study of human and rodent ears, we measured the magnitude of more than one cubic distortion component (2fl-f2, 3fl-2f2, etc.) while varying stimulus frequency separation. We found that the magnitude of each of the cubic distortion

components reaches a maximum when the distortion

frequency is just over half an octave below the high- frequency stimulus for a wide range of stimulus conditions in both rodent and human ears (Brown & Gaskill 1990b). In each case, stimulus frequency separation for the two primary frequencies is different. This was a surprising finding and it implies that distortion level is not dependent simply on stimulus

frequency separation, but that the frequency of the distortion itself is critical.

The common frequency for the distortion magnitude peak led us to suspect that the distortion components were being filtered within the cochlea subsequent to their generation at the stimulus site. This would mean that there is a fairly broadly tuned filter within the cochlea which has a centre frequency well below that of the stimulus frequencies. Such an idea is a novel one that does not fit well with most current theories of cochlear mechanics. Therefore, to confirm and extend our previous findings, we undertook the following experiments in which both magnitude and phase of two cubic distortion components were measured. If both magnitude and phase showed significant corre-

spondence between distortion components when

compared as a function of distortion frequency, our contention that we are observing the output of a band-

pass filter would be strengthened and we would have

? 1992 The Royal Society



30 A. M. Brown and others Mechanical filtering of sound

distance along cochlear partition > base

f2

s a

0

bi) 0

region of distortion

generation

propagation towards base of cochlea giving rise to emission

propagation as travelling waves towards apex

giving rise to audible distortion

Figure 1. Log displacement as a function of distance along the cochlear partition caused by the two stimulus tones at moderate levels. The vibration reaches a maximum for f2 more basally than for f 1. Distortion is generated at the

region of stimulus overlap and propagated apically to the appropriate place for the distortion frequency on the basilar membrane (shown as two separate travelling waves) and basally to the middle ear to give rise to the measured emission.

grounds for speculation about the location of this filter and the structures responsible.

2. METHOD

The four human subjects (one female, three male) used in these experiments were aged between 20 years and 30 years. Their audiometric thresholds were within 20 dB of normal between 500 Hz and 8000 Hz as measured by a two- alternative forced-choice procedure based on that of Levitt

(1971). The two stimuli were delivered through miniature loud-

speakers in a specially constructed ear canal probe. The

probe also housed the microphone used to detect the ear canal sound pressure. Distortion levels are substantially below those of the stimuli (20 dB to 60 dB below), so we used a 'lock-in' amplifier (EG&G 5210) to give the necessary sensitivity and immunity to interference from the stimulus tones. An artificially generated distortion signal was fed as a

phase reference to the amplifier. This allowed us to derive the

magnitude of each distortion component emitted and its

phase relative to that of the reference signal. The phase of the artificial distortion was derived from the stimulus waveforms while maintaining the original phase relation. Thus a zero

phase reading for artificial 2f l-f2 would occur when both f2 and fl phases were zero. The higher-frequency stimulus (f2) was fixed at 4 kHz and at a level of 40 dB SPL, whereas fl was swept (at a fixed level 15 dB above the level of f2) from 2837 Hz to 3960 Hz to give a 'ratio sweep'. The choice of 4 kHz for f2 was made for three main reasons: (i) most people have easily measurable levels of distortion in this frequency region and there is a good chance of detecting 3f -2f2 as well as 2fl-f2; (ii) the probe microphone is maximally sensitive in this region; and (iii) the background acoustic noise is

relatively low at high frequencies. A range of f2 frequencies was used in our previous studies (Brown & Gaskill 1990 a, b). The range of stimulus frequency separation was chosen from

previous studies to encompass the range over which the distortion magnitude peak was known to occur (Harris et al. 1989; Gaskill & Brown 1990). This ratio sweep was done on four subjects for two distortion components (2fl-f2, then

a-' C/)

a) -IO a a 0F 'a

b0

cli a a)

a)

a) a)

00

a)

-u a) Cl)

4)

(a -a VI

4-4

20-

0'

-20

(a)

2000 2500 3000 3500 4000

2fl-f2 frequency / Hz

Figure 2. (a) Magnitude and (b) phase of a single trace of 2f 1- f2 distortion measured from subject B as the frequency of f was swept from 2837 Hz to 3960 Hz at a level of 55 dB SPL. F2 was fixed at 4 kHz at a level of 40 dB SPL. The noise floor is indicated by rapid unsystematic changes in phase readings: in this case it occurs when the magnitude is about -15 dB SPL.

Proc. R. Soc. Lond. B (1992)

apex



Mechanical filtering of sound A. M. Brown and others 31

3fl-2f2) on up to four successive occasions over a 6-week period. During the subsequent data analysis, the phase readings were 'unwrapped' to give a continuous slope over several cycles of phase lag and smoothed using a 41-point moving average. It was then possible to calculate the mean group delay of the distortion by measuring the slope of distortion phase lag as a function of distortion frequency (-d0/dw).

3. RESULTS

Raw data from one subject's ratio sweeps (subject B; magnitude and phase for 2fl-f2) is shown in figure 2. The magnitude of distortion reaches a maximum at

frequencies between 2500 Hz and 3000 Hz, and the

phase passes through four complete cycles relative to that of the reference signal.

All ratio sweeps for all subjects are shown in figure 3 where the phase has been 'unwrapped' to give a continuous phase slope. The main findings are sum- marized in table 1.

The magnitude plots for each ear (figure 3, top) show that distortion level reaches a maximum when the distortion frequency falls between 2600 Hz and 2800 Hz. The mid-frequency for this peak was obtained

by fitting a second-order polynomial to the magnitude

10 -

-10 - 4MRN A-

-E0

B

curves for 2fl-f2 and 3fl-2f2. In one subject (A), the 3f 1-2f2 response was too near the noise to allow similar

treatment, but it can be seen to protrude above the noise floor over a similar frequency range to that of 2f 1- f2. There is good agreement in the frequency at which the two distortion components reach a peak level (table 1). This peak varied between subjects from 0.5 to 0.6 of an octave below f2, which is in agreement with our

previous findings (Brown & Gaskill 1990b). There is also some agreement between distortion components in the fine structure of the magnitude curves, although there is a tendency, particularly marked in subject D, for the peaks in 3fl-2f2 fine structure to be shifted towards lower frequencies than for 2fl-f2.

The phase of distortion measured across the same

frequency range as the magnitude for each of the four

subjects (figure 3, below) shows a progressive phase lag as the frequency of fl (and hence the distortion

frequency) increases. There is clear agreement between the slopes for 2f 1-f2 and 3f1-2f2 in all subjects over the

frequency range of the magnitude peak, but the slope of 3fl-2f2 tends to be steeper than that for 2fl-f2 towards the high-frequency end of the graph.

The mean group delay for the frequency region of the peak is shown for each subject in figure 4. The

graphs show that mean group delay for components,

C D

2000 3000 4000 2000 3000 4000 2000 3000 4000 2000 3000 4(

frequency of distortion / Hz

Figure 3. Magnitude (above) and phase (below) of distortion measured from all four subjects (A, B, C & D) for the same stimulus parameters as figure 2. In subjects B, C, and D, two sets of readings for 2f -f2 and 3f1-2f2 are shown for two measurements sessions 1 week or 2 weeks apart. Data from A was from a single measurement session. Arrows above the magnitude trace indicate the frequency one half octave below f2. Traces show 2fl-f2 (solid lines) and 3fl-2f2 (broken lines).

Table 1. Frequency of magnitude peak (calculatedfrom 2nd-order polynomialfit) and mean of mean group delay (data range shown in figure 3) for 2fl-f2 and 3fl-2f2 in subject

2fl-f2 3f1-2f2 2f -f2 peak 3fl-3f2 peak delay 2fl-f2 delay 3fl-2f2 subject peak/Hz peak/Hz re f2/octaves re f2/octaves (s.d.)/ms (s.d.)/ms

A 2679 2650a -0.58 -0.59a 2.25 (0.35) 2.27 (1.83) B 2789 2800 -0.52 -0.52 2.3 (1.00) 2.99 (1.37) C 2807 2733 -0.51 -0.55 3.11 (1.04) 3.57 (1.29) D 2824 2741 -0.5 -0.55 3.48 (1.15) 3.94 (1.97)

a Approximate value.





A B

ciz 1-4

ci

a, lc 0)

Sb

C

2600 2900

D

frequency of distortion / Hz

Figure 4. Mean group delay computed from sections of the phase traces shown in figure 3 where a slope is clearly measurable. Traces show 2fl-f2 (solid lines) and 3f I + 2f2 (broken lines).

2f -f2 and 3fl-2f2, is the same over most of the range where phase can be measured, although 3fl-2f2 was nearer the noise floor and produced a noisier trace.

There are some frequencies (such as 2900 Hz in B) where there is a noticeable difference in the delay for the two distortion products and there is a tendency to

greater delay for 3f 1-2f2 at high frequencies (= smaller f2:f 1 ratios). The mean of the mean group delay across the measurable range is between 2 ms and 4 ms and is shown in table 1. The tendency towards greater phase lag at high frequencies for 3fl-2f2 than 2fl-f2 gives rise to slightly larger overall mean delay for 3fl-2f2 for three subjects.

4. DISCUSSION

Our observation (Brown & Gaskill 1990b) that all distortion components achieved a peak in their

magnitude at a common frequency related to f2, irrespective of the separation of the two stimulus

frequencies, led to the idea that distortion components are band-pass filtered in the cochlea. The present results confirm the original findings by showing that the magnitude of distortion reaches a peak when the distortion frequency is a little over half an octave below f2. This is shown for the two cubic distortion

components, 2fl-f2 and 3fl-2f2 in all four subjects. This coincidence of distortion peak frequencies was also noted by Fahey & Allen (1985). The present results also show fine structures in the magnitude of the two distortion components which correspond reason-

ably well across frequency, providing further cor- roborative evidence for a single band-pass filter. The remarkable similarity between the phase slopes for the two distortion components suggests that the com-

ponents have a common delay and are likely to be

coming from the same place. The evidence clearly points to a filter centred at a frequency which is related to, but lower than, f2. Where and what is this filter?

The association with the f2 frequency suggests that this filter may be operating at the f2 site. If the distortion is travelling directly from the stimulus region to the base of the cochlea, it will not encounter any further frequency-selective mechanical structures which would filter the distortion in the way we have described. However, we know that distortion propagates apically as well as basally, each component

behaving like a pure tone stimulus to the ear, producing its own travelling wave, eliciting a tuned response (Kim et al. 1980) and resulting in the perception of cubic distortion (Smoorenburg 1972). Some re- emission of energy to the meatus is also known to occur from this more apical region where the distortion

frequency reaches a maximum (Wilson 1980). The common behaviour of distortion as a function of distortion frequency could be explained by assuming that the distortion propagates from the stimulus region to the distortion product region and is then re-emitted to the ear canal from this secondary site. Three observations make propagation from the distortion

product site an unlikely explanation. 1. The delay is too short: estimates of the time

required for re-emission from a region tuned to 2.6 kHz

(the distortion peak) are 5 ms or greater when a tone of that frequency is used as the stimulus (Wit & Ritsma

1980). The same authors recorded latencies of 4 ms down to 1.5 ms for 4 kHz tone re-emission (our f2

frequency and the presumed site of distortion generation). The latter figures compare with our range of 2-4 ms (for distortion around 2.6 kHz generated by a 4 kHz f2).

2. If the distortion was being emitted from progressively nearer the base as the frequency of f 1 swept from low to high, there would be a diminution in delay as the travel time within the cochlea became less with

increasing distortion frequency. The results do not show such a trend.

3. It would not explain why distortion is emitted so well when its own frequency is half an octave below f2.

The short emission delay, the fact that this delay is

fairly constant across frequency, and the close relation

(half octave) between the frequency of the distortion maximum and f2 regardless of which distortion component is being measured, together suggest that the majority of the distortion we have measured in the ear canal in these experiments has been generated then filtered at the f2 region on the cochlear partition.

What is the filter? The basilar membrane acts as a

band-pass filter, but it is tuned to f2 at the f2 place, not to a frequency half an octave below this. Another structure which is intimately involved in the transduction process is the tectorial membrane (TM). The basilar membrane is linked to the TM through the outer hair cells and their stereocilia. In the Ter Kuile (1900) model of cochlear mechanics, the movement of the




Mechanical filtering of sound A. M. Brown and others 33

tectorial membrane relative to the basilar membrane

provides a radial shear action which deflects the stereocilia. The displacement of stereocilia is known to

open transducer channels (Howard et al. 1988). Only the outer hair cell stereocilia are firmly embedded in the tectorial membrane. The inner hair cell stereocilia are attached lightly or not at all to the tectorial membrane (Steel 1983) and are probably deflected by the flow of fluid in the subtectorial space, rather than

by direct displacement by the TM. The inner hair cells are almost entirely responsible for providing the afferent output from the cochlea to higher auditory centres.

Some workers have advocated a role for the TM in

improving the sharpness of 'tuning' of the afferent

response to sound (Zwislocki & Kletsky 1979; Allen

1980). Little is known of the mechanical properties of the TM, except that its stiffness is an order of magnitude less than that of the outer hair cell stereocilia (Zwislocki & Cefaratti 1989; Strelioff 1985), but the complex radial organization in the ultrastructure of this membrane (Hasko & Richardson 1988) makes the notion of some selectivity in its frequency response along the cochlear partition very plausible. Allen

(1980) has included the mass of the TM and the

elasticity of its attachment to the cochlear bone in his model of cochlear mechanics. He predicts that the resonance frequency for the TM would be below that of the BM at any one point on the cochlear partition. Thus, the radial motion of the partition would include two resonances: that of the sharply tuned response of the basilar membrane at the frequency characteristic of that place, and that of the tectorial membrane tuned to a lower frequency. As the TM is connected to the BM

through the outer hair cells, vibration at frequencies below the local characteristic frequency may find an alternative path through the TM to the cochlear fluids, largely bypassing the subtectorial space. The inner hair cells are stimulated by fluid movement in the subtectorial space, so they would receive maximum stimulation at the characteristic frequency as this would be transmitted in full to the subtectorial space. Vibration below this would tend to be diverted away from the subtectorial space providing relatively little stimulation to the inner hair cells.

It may be possible to explain the remarkable behaviour of distortion that we have described by imagining that, when two tones are delivered to the

ear, some of the resulting intermodulation distortion falls within the pass-band of the putative tectorial membrane filter. A proportion of the distortion would

pass directly through the tectorial membrane to the cochlear fluids instead of stimulating the inner hair cell stereocilia in the subtectorial space. The distortion would propagate directly to the base of the cochlea and thence to the ear canal. In this case the distortion

magnitude as a function of frequency which we have recorded in the ear canal will reflect the frequency response of the tectorial membrane at the place where the basilar membrane is tuned to f2. We can then infer that the tectorial membrane is tuned to a frequency half an octave or more below that of the basilar membrane.

If we ignore for the time being any active con- tribution that the outer hair cells might make to the BM

response, then, if the TM acts in the manner proposed, the inner hair cells would receive a band-pass filtered stimulus instead of the low pass filtered stimulus that the passive BM response alone would supply. This would be an elegant solution to the problem of

achieving frequency selectivity in a system whose

passive properties are essentially low-pass in nature. Our demonstration of the presence of a structure which is tuned to a frequency below that of the basilar membrane raises the possibility that such a mechanism could operate in the mammalian cochlea.

This work was supported by MRC project grants to A. M. B. and S.A.G. and a Wellcome grant to D. M.W. The sound- treated room and some equipment were provided by the Hearing Research Trust. We are grateful to Jont Allen of A. T. & T. Bell Labs for stimulating discussion, and to Brian Warburton, who designed and built the artificial distortion source. We would also like to thank several reviewers for their contributions to this manuscript.

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Received 18 June 1992; accepted 27 July 1992




mechanical filtering of sound in the inner ear

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