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The Effect of the Helicotrema on Low-Frequency Cochlear Mechanics and Hearing

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At very low frequencies, when the travelling wave reaches the apical end of the cochlea, perilymph is forced through the helicotrema. Iso-modulation curves of distortion product otoacoustic emissions (DPIMCs) reveal non-invasively the frequency-dependence of low-frequency sound transmission onto the basilar membrane, and demonstrate that this shunting contributes in humans to the steep decline in hearing sensitivity below 40 Hz. Just above, an irregularity often indicates a resonant interaction between perilymph inertia in the helicotrema and apical basilar membrane compliance. Anticipating an effect of this resonance on sound perception, we measured DPIMCs and equal-loudness contour (ELC) between 20 and 160 Hz in 14 subjects. A pronounced (non-monotonic) resonance was visible in 16 DPIMCs of 26 measurable ears, and nine of the 14 ELCs. Eight subjects of the 12 bilaterally measurable subjects had similar DPIMC in both ears. DPIMCs and ELC of approximately half the subjects were clearly related.
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The Effect of the Helicotrema on Low‐Frequency Cochlear Mechanics and Hearing
Torsten Marquardt and Carlos Jurado
Citation: AIP Conference Proceedings 1403, 495 (2011); doi: 10.1063/1.3658137
View online: http://dx.doi.org/10.1063/1.3658137
View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1403?ver=pdfcov
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The Effect of the Helicotrema on Low-Frequency
Cochlear Mechanics and Hearing
Torsten Marquardtand Carlos Jurado
UCL Ear Institute, University College London
Department of Electronic Systems, Aalborg University
Abstract. At very low frequencies, when the travelling wave reaches the apical end of the cochlea,
perilymph is forced through the helicotrema. Iso-modulation curves of distortion product otoacous-
tic emissions (DPIMCs) reveal non-invasively the frequency-dependence of low-frequency sound
transmission onto the basilar membrane, and demonstrate that this shunting contributes in humans
to the steep decline in hearing sensitivity below 40 Hz. Just above, an irregularity often indicates
a resonant interaction between perilymph inertia in the helicotrema and apical basilar membrane
compliance. Anticipating an effect of this resonance on sound perception, we measured DPIMCs
and equal-loudness contour (ELC) between 20 and 160 Hz in 14 subjects. A pronounced (non-
monotonic) resonance was visible in 16 DPIMCs of 26 measurable ears, and nine of the 14 ELCs.
Eight subjects of the 12 bilaterally measurable subjects had similar DPIMC in both ears. DPIMCs
and ELC of approximately half the subjects were clearly related.
Keywords: low frequency hearing, helicotrema, equal loudness contours
PACS: 43.64.Kc, 43.66Cb
INTRODUCTION
The helicotrema determines ultimately the lower frequency end of cochlear sensitivity.
It prevents not only displacement of the cochlear partition in response to static pressure,
but alters hearing sensitivity to low-frequency sounds as differential pressure across the
cochlear partition is shunted. Dallos [1] showed that the impedance of the helicotrema
shunt has species-dependent characteristics. In cat and chinchilla, the slope of the for-
ward middle-ear transfer function (fMETF) increases by 6 dB/octave below approxi-
mately 100 Hz, indicating that the oscillatory perilymph flow through cochlear ducts and
helicotrema is here inertia-dominated. In contrast, cochleae of guinea pig and kangaroo
rat exhibit more turns, more tapering, and a smaller helicotrema, so that this perilymph
movement in these cases is dominated by viscous friction. Therefore, the fMETF of these
two species has the same slope at frequencies below and within the existence region of
the resistive travelling wave. These two frequency regions can be easily distinguished
in the data of all four species by a resonance feature, separating them at approximately
100–150 Hz.
Recently, a non-invasive technique was described that is based on the suppression of
distortion product otoacoustic emissions (DPOAE) and enabled the assessment of the
fMETF characteristics up to 500 Hz in humans and guinea pig [4]. The shape of the
resulting distortion product iso-modulation curves (DPIMC) of the guinea pigs agreed
with those of previously published, invasively obtained fMETFs. The human curves
followed roughly the equal loudness contour at 80 phon (ISO 226: 2003). However,
What Fire is in Mine Ears: Progress in Auditory Biomechanics
AIP Conf. Proc. 1403, 495-501 (2011); doi: 10.1063/1.3658137
© 2011 American Institute of Physics 978-0-7354-0975-0/$30.00
495
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whilst these standardized contours indicate a smooth monotonic increase of sensitivity
with tone frequency (<1 kHz); the DPIMC exhibited a non-monotonic resonance feature,
below which the slope changes rather sharply by 6 dB per octave. The shape of the
resonance feature in humans were similar to those observed in the four species studied
by Dallos, but appeared approximately an octave lower, implying that in humans the
shunting by the helicotrema becomes fully effective below approximately 40 Hz. The
resonance is presumably caused by the oscillatory interaction between basilar membrane
(BM) stiffness and inertia related to the flow of perilymph through the helicotrema [3].
The increased slope below the resonance frequency supports Dallos’ anatomy-based
conjecture that the impedance of human cochlea is inertia-dominated at the lowest
frequencies.
Surprisingly, a recent review of low-frequency hearing threshold and equal- loudness-
contours (ELC) [6] does neither reveal a convincing behavioral homologue to the res-
onance, nor the sharp steepness increases. Our suspicion is that the frequency of the
resonance might vary individually so that in these studies the process of averaging over
many subjects might have led to cancellation of individual features. Therefore, we de-
cided to measure both DPIMC and ELC, and compare their features on an individual
basis. A pilot study on five subjects was previously reported [5].
METHODS
A group of 10 male and 4 female subjects with normal hearing (125 to 4000 Hz: 20 HL,
or better) participated in both the DPIMC and ELC experiments.
Objective measurements of fMETF shapes
Details of this method are published elsewhere [4]. Here a brief summary: For low-
frequency tones within a frequency range of 20–250 Hz, DPIMCs were obtained by
adjusting their level, so as to evoke constant BM displacement amplitude. The latter
was monitored by simultaneously measuring the 2 f1f2distortion product otoacous-
tic emission (DPOAE), which was suppressed periodically with the frequency of the
BM displacement. The method is based on the assumption that a constant DPOAE sup-
pression depth indicates a constant BM displacement (independent of the suppressor
frequency). Because the BM displacement is monitored at a location that is far basal
from the characteristic place of the suppressor tone, the produced BM displacement
is stiffness-controlled, and therefore, proportional to the pressure difference across the
BM. Consequently, the fMETF, whose shape is reflected in this iso-modulation function,
is defined here as the ratio between this pressure difference and the pressure in the ear
canal. Note that, all illustrated DPIMC data are, like the behavioral ELC data, obtained
as an iso-output function, and represent therefore the inverse of the fMETF. It has been
shown previously that the shape of the fMETF, which is of interest here, is unaffected
by the chosen DPOAE suppression depth and the primary parameters [4]. To maximize
2f1f2level, the primary parameters have been chosen individually for each ear from
18 primary combinations, tested in a short series of 5-s recordings immediately prior to
the DPIMC measurement in this ear. ( f2={2215,2515,2715}Hz; f2/f1={1.2,1.22};
l2=50 dB SPL; 11={62,65,68}dB SPL). DPIMCs were only measured for ears with
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unsuppressed 2 f1f2DPOAE levels larger than 5 dB SPL. The chosen DPOAE sup-
pression depth varied amongst ears, ranging 4–9 dB.
DPOAEs were measured with an Etymotics ER-10C probe. The high-pass cut-off
frequency of its microphone amplifier was increased to 1 kHz in order to avoid over-
loading the AD converter of the multi-channel sound card (MOTU UltraLite) with the
comparatively intense low-frequency modulating tone. This tone was produced by a DT-
48 earphone (Beyerdynamic) that was directly driven by the headphone amplifier of the
soundcard. The earphone output was delivered into the ear canal via a custom-made
adaptor to a narrow silicone tube (200 mm in length, 0.5 mm i.d.), which was fed
tightly through the pierced ear plug of the ER-10C probe. Stimulus waveform gener-
ation and DPOAE signal analysis was performed using custom-made software. After
displaying two periods of the 2 f1f2suppression pattern, averaged over a 20-s long
recording, the suppressor tone level for the next 20-s recording could be adjusted by
the experimenter. This was repeated until the desired DPOAE suppression depth was
achieved, typically using 3 or 4 recordings. Measurements of both ears were obtained
in a single session usually lasting less than 1.5 hours, including a short break when
changing to the other ear.
Equal-loudness-level contours
Equal-loudness-level contours, using a 50-Hz reference tone, were obtained for the
same subjects from 20 to 160 Hz within a test chamber (0.8×1.4×0.9 m), purpose-
built for the playback of low-frequency signals under pressure field condition. Each side
wall contained four Seas 33 F-WKA 13-inch loudspeakers driven by a Crown Studio
Reference I (1160 W) power amplifier. Up to approximately 60 Hz, the cabin provides a
pressure field within its overall volume. Before the experiments commenced, calibrated
measurements ensured a flat transfer function within the range of possible head positions
(±3 dB up to 150 Hz), and inaudibility of harmonic distortions and external sounds
caused by usual activity in the building.
Just before each ELC measurement, a 3-alternative forced-choice task with a 3- down
1-up adaptive procedure was used to estimate the detection threshold for a 50 Hz tone
in order to set this reference stimulus in the ELC measurement individually to 40 dB
SL. The stimuli were 1.2 sec long, including 0.2 sec linear on- and offset ramps. Their
timing was indicated by illuminating the response button corresponding to each interval.
The inter-interval gaps were 400 ms. Feedback was provided after each response by
illuminating the correct button. The procedure started at 15 dB HL with a simple 1-
down 1-up rule for the first four presentations in order to rapidly approach the region
of detection threshold. The initial stepsize of 8 dB was decreased to 4 dB and later to
2 dB, each after 2 reversals. The procedure terminated after 8 further reversals and the
threshold was estimated by averaging these 8 reversal levels. Two threshold estimates
were obtained. If they differed by more than 3 dB, a third estimate was obtained. The
two closest values were averaged to estimate the detection threshold.
Equal loudness was adjusted using a 2AFC task with a 1-up 1-down adaptive loudness
balance procedure. Stimulus timing and inter-stimulus interval were identical to those
described above. The reference and comparison tone were presented in random order,
and the subject was asked to press the button associated with the louder stimulus interval.
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FIGURE 1. Individual DPIMCs and ELCs obtained for 14 subjects. The mean DPIMC and ELC
curves are shown as bold lines. For comparison, isophons [2] are shown as dashed lines.
Two interleaved tracks were used. For a given comparison tone, the level of one track
started 10 dB below, the other 10 dB above the 40 phon standardized equal-loudness
contour [2] (exception at 20 Hz: ±5 dB). The initial stepsize of 8 dB, was decreased
to 4 dB and later to 2 dB, each after 2 reversals. Each track terminated after 6 further
reversals and the point of subjective equality (PSE) was estimated by averaging these
6 reversal levels. The PSE of the run was calculated as the average PSE of the two
interleaved tracks. Two runs were performed. If their PSEs differed by more than 3
dB, a third run was performed. The (2 or 3) PSEs were averaged to determine the
subject’s PSE for the two frequencies tested. Short breaks took place regularly after
every second run (about every 5 to 8 minutes) to maintain the subject’s attention. The
psychoacoustical measurements were obtained in a single session, lasting about 2½
hours in total, including breaks.
RESULTS AND DISCUSSION
The DPIMCs of all 14 subjects could be obtained, although for subjects 7 and 14 only
in one ear. The left ear of subject 7 emitted DPOAE levels that were considered too low
for a reliable DPIMC analysis (<5 dB SPL). The DPOAE of subject 14’s right ear could
not be sufficiently modulated by low-frequency tones below 90 phon. Fig. 1 shows on
a dB SPL scale an overview of all data obtained. Most DPIMC (thin lines, no marker)
follow roughly the 80-phon curve. However, the average curve (bold) indicates clearly
a transition from the 70-phon curve below 40 Hz to the 80-phon curve above 60 Hz.
Consistent with the curved shape of the isophons, these frequency regions also differ
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FIGURE 2. DPIMCs, obtained from the subject’s the left (dashed) and right (solid) ears, are
shown grouped together with the subject’s ELC (bold). For clarity, curves of different subjects are
offset.
in their slope (20–35 Hz: 13 dB/octave, 100–250 Hz: 6 dB/octave). Individual curves
commonly exhibit a resonance feature that separates the two regions. As a consequence
of the considerable variability in subject’s detection threshold for the 50-Hz reference
tone (2–47 dB SPL, mean 39.3 dB SPL), individual ELCs (thin lines with dots) were
spread widely, around 20 to 60 phon. Some of the individual ELCs reflect the resonance
feature exhibited by the majority of DPIMCs. Its appearance in the average ELC (bold
with dots) is, however, rather subtle compared to that in the average DPIMC. The
average ELC follows roughly the 40- phon curve, although also here, a marked transition
from clearly below to well above this isophon curve is evident. A rather abrupt change
in slope at 40 Hz (20–35 Hz: 22 dB/octave, 50–160 Hz: 9 dB/octave) contrasts the
smoothness of the standardized isophons [2]. Consistent with the loudness-dependent
slope change of the standardized isophons, the ELCs were notably steeper than the
DPIMCs.
Figure 2 shows DPIMCs and ELCs of individual subjects grouped together and there-
fore on an arbitrary dB-scale. The left panel contains DPIMCs that show the classic non-
monotonic irregularity, as observed in all previously measured ears [4,5]. The curves
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of the individual subjects are here ordered by decreasing resonance frequency, show-
ing a inter-individual variability of approximately 2/3 octaves. The slope of individual
DPIMCs below the resonance feature is generally steeper than in the region above. This
increased sensitivity loss towards lowest frequencies is an indication of the pressure-
shunting effect of the helicotrema [3]. The sharpness of this transition is often empha-
sized by the lower-frequency dip of the resonance feature. The DPIMCs of subjects,
plotted in the right panel, exhibit no, or a less pronounced resonance in either one (sub-
jects 9, 10, and 11) or both (subjects 8, 12, and 13) of their ears. Subject 14’s left ear
and the right ear of subject 12 show rather unusual double resonances. Left and right
ear DPIMCs of eight of the 12 bilaterally measurable subjects were of similar shape.
Across-ear symmetry can therefore not be generalized. Asymmetries can be observed in
center frequency (subjects 5 and 10), as well as in damping of the resonance (subjects 2,
3, 6, 9, 10, and 11).
With the exception of subjects 2 and 14, the obtained ELCs deviated generally from
the smoothly curved standardized isophons [2] by exhibiting rather abrupt slope transi-
tions, or a non-monotonic irregularity, similar to those in the DPIMCs. The ELC irregu-
larity was for many subjects (1, 4–7, 11) in agreement with that in their DPIMC. Subjects
10, 12, and 14 showed consistently highly damped resonance in both, their DPIMCs and
ELC. Subjects 2, 9, and 13 had clear inconsistencies between both measures. E.g., the
ELC of subject 2 was very smooth despite having matching resonances in the DPIMCs
of both ears. Consistent with the loudness-dependent slope change of the standardized
isophons [2], the slope of the ELC, obtained with a 40 dB SL reference tone, was for
most subjects shallower than those of their DPIMCs, measured near 80 phon.
CONCLUSIONS
1. This study of low-frequency sound transmission onto the basilar membrane reveals
notable inter-individual differences.
2. The results show that detailed features in the fMETF can affect and might explain
individual differences in low-frequency sound perception.
3. Standardized ELCs [2] do not reflect the irregularities and abrupt changes in slope
as observed in the current study, and seem therefore very simplified.
4. At this time, the authors cannot explain the occasionally observed inconsistencies
between individual fMETFs and ELC.
REFERENCES
[1] Dallos P (1970) Low-frequency auditory characteristics: Species dependence. J Acoust Soc Am
48:489–499
[2] ISO 226 (2003) Acoustics—normal equal-loudness contours. International Organization for Stan-
dardization
[3] Marquardt T, Hensel J (2008) A lumped-element model of the apical cochlea at low frequencies. In:
Cooper NP, Kemp DT (eds) Concepts and Challenges in the Biophysics of Hearing, London: World
Scientific. pp. 337–339
[4] Marquardt T, Hensel J, Mrowinski D, Scholz G (2007) Low-frequency characteristics of human and
guinea pig cochleae. J Acoust Soc Am 121:3628–3638
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[5] Marquardt T, Pedersen C S (2010) The influence of the helicotrema on low-frequency hearing.
In: Lopez-Poveda EA, Palmer AR, Meddis R (eds) The Neurophysiological Bases of Auditory
Perception, New York: Springer. pp. 25–36
[6] Møller H, Pedersen CS (2004) Hearing at low and infrasonic frequencies. Noise Health 6:37–57
COMMENTS AND DISCUSSION
Paul Teal: A very interesting paper.
1. Some details of the fMETF measurement procedure are a bit obscure—in particular, how do you
know what location is being monitored?
2. The equal loudness level contours are established under “pressure field conditions” in a test cham-
ber. Why is this? Given that the fMETF measurements are conducted separately for each ear (using
an ear phone and pierced ear plug), why not do the equal loudness level tests also separately for
each ear and under similar conditions. Would not this make the comparison more valid?
Reply: Thanks for your comments.
1. It is most likely that we monitored the BM displacement close to the CPs of the DPOAE primaries
(about the mid-way between base and apex, i.e., well remote from the helicotrema).
2. Regarding the “pressure field conditions” during the ELC measurements, I agree that this is unfor-
tunately somewhat of a weak point in our study. However, the ELC data collection was also used in
a critical band study (see Jurado et al. 2011 J Acoust Soc Am 129:3166–3181), where they had al-
ready decided to do all experiments binaurally. It is pretty difficult to produce clean LF-tones at the
required SPLs with standard headphones. I agree that an ear-by-ear comparison would be stronger,
and we could have used the same system as for the DPIMC measurements. But the binaurally ob-
tained ELC were collected anyway, and we believe that the current comparison shows already a
surprisingly strong perceptual effect of the helicotrema for many subjects and therefore conveys the
point we intend to make.
John Rosowski: I enjoyed your presentation. However, I think you overlooked a possible source of the
compliance you needed for the low-frequency resonance. Lynch et al. (1982 J Acoust Soc Am 72:108–
130) measured the cochlear input impedance of the cat and came to the conclusion that the round window
played a role at very low frequencies. They put together a simple model of the low-frequency cochlea
which included the round window. This model fit the data of Dallos [1] as well as the low-frequency
auditory data of Miller et al. (1963, Acta Otolaryngol Supp 176:1–91) Maybe you could mention the
possibility that a compliance of the round window might also fit your data.
Reply: Thanks John. Although the round window determines the cochlear input impedance at very low
frequencies, it has no effect on the differential pressure across the BM (Nedzelnitsky 1980 J Acoust
Soc Am 68:1676–1689). This view is commonly observed in electrical equivalent circuits (e.g., Lynch et
al., op. cit.; Franke and Dancer 1982 Arch Otorhinolaryngol 234:213–218), which incorporate the round
window stiffness in series with the elements representing the cochlear partition and helicotrema (over
which the differential pressure is estimated ). The stiffness associated with the discussed resonance feature
must be in parallel with the mass impedance that represents the perilymph flow through the helicotrem:
At stimulus frequencies lower than the resonance, it is the mass and not the stiffness that dominates the
differential pressure across the BM (as seen by the 12 dB/octave slope in the human, chinchilla, and cat
data). Most likely, the BM provides this parallel stiffness. Lacking such, the model by Lynch et al. fails
to reproduce the discussed resonance at 150 Hz (their Fig. 24: model comparison with Nedzelnitsky’s
cat data), and so does the model by Franke and Dancer because theirs lacks a mass-element. Since our
experiments assess only the differential pressure across the BM, we omitted the round window in our
model (see [3]).
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... Jurado and Marquardt (2016) reported that low-frequency ELCs were similar in shape to iMETFs, and that step frequencies for the two were similar and were highly correlated (R 2 % 0.9). The characteristics of the METF have in turn been explained as an effect of the helicotrema on apical cochlear mechanics for both humans and animals (see, e.g., Marquardt et al., 2007;Marquardt and Jurado, 2011;Marquardt and Hensel, 2013). ...
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