Basilar Membrane Vibration in the Gerbil Hemicochlea

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Basilar Membrane Vibration in the Gerbil Hemicochlea
CLAUS-PETER RICHTER, 2 BURT N. EVANS, 1 ROXANNE EDGE, 1 AND PETER DALLOS 1
1
Departments of Neurobiology and Physiology and Communication Sciences and Disorders, Auditory Physiology
Laboratory (The Hugh Knowles Center), The Institute of Neuroscience, Northwestern University, Evanston, Illinois
60208; and 2Zentrum der Physiologie, J.W. Goethe-Universität, Theodor-Stern-Kai 7, 60590 Frankfurt/Main, Germany
INTRODUCTION
Propagation of mechanical disturbances (traveling waves)
along the basilar membrane in the cochlea has been studied
experimentally for about half a century. As the traveling
wave proceeds along the cochlea, from base toward apex,
tones of different frequencies produce waves that rise in
amplitude at different rates and attain their maxima at different locations before extinguishing. Thus the traveling wave
functions as a spatial spectral analyzer. Further, the speed
of transmission of the wave along the basilar membrane is
slow compared with the propagation velocity of sound in
fluid.
von Békésy (1928, 1960) first experimentally observed
the traveling wave on the basilar membrane of human cadaver ears. Such waves also have been described for other
classes. Beside mammals, a traveling wave has been found in
birds (Gummer et al. 1987; von Békésy 1960) and alligators
(Wilson et al. 1985). For mammals, the quantitative properties of traveling waves are now well established (Rhode
1971; Robles et al. 1986; Sellick et al. 1982; von Békésy
1960). For all cases, the direction of wave travel is from
base to apex. Efforts to evoke wave travel towards the basal
end of the cochlea, by moving the ‘‘stapes’’ to the apex,
have not been successful. Regardless of the position of the
stapes or artificial stapes, the wave propagation is in a baseto-apex direction (von Békésy 1928; Wever and Lawrence
1954). The explanation of this phenomenon is that no matter
where acoustic energy is delivered into the cochlear fluids,
traveling waves occur after the energy is transmitted to the
inner ear fluids, and the direction of wave travel is determined by the mechanical properties of the basilar membrane
(von Békésy 1928). The basilar membrane possesses exponentially graded stiffness, so that the base is some 100fold stiffer than the apex (von Békésy 1960). Thus wave
propagation is evidently unidirectional toward the more
compliant region when input energy is delivered via the
surrounding fluid.
The simple notion of resonance of the basilar membrane
is based on the assumption that the longitudinal tension of
the membrane is negligible. However, the question of
whether longitudinal coupling is present in the basilar membrane is controversial (Vôldrich 1978; von Békésy 1960).
Existence of longitudinal coupling has been supported experimentally by von Békésy (1960) and has been considered
in some cochlear models (Allen and Sondhi 1979; Wickesberg and Geisler 1985). Inclusion of longitudinal coupling
in cochlear models broadens the tuning curve at its tip, as
demanded by experimental observations. In other words,
longitudinal coupling is incorporated to make modeling efforts conform more closely to physiological observations
(Wickesberg and Geisler 1985). However, minimal longitudinal coupling in the basilar membrane has been observed
experimentally (Vôldrich 1978). Furthermore, other modeling efforts of the basilar membrane suggest that inclusion
of longitudinal coupling reduces the tuning predicted by the
model (Allen and Sondhi 1979).
A lack of longitudinal coupling in the basilar membrane
would not permit propagation of energy in the basilar membrane itself. Consequently, in this case, all acoustic energy
has to be coupled through the cochlear fluids. Interesting
questions of how energy corresponding to internally generated signals, such as otoacoustic emissions is back-propagated to the stapes or how combination tones are distributed
remain largely unanswered.
In the case of combination tones, it is assumed that energy
is generated at one place on the basilar membrane and propagates as a traveling wave to the basilar membrane site with
a characteristic frequency equal to that of the combination
tone (Goldstein 1968; Siegel et al. 1982; Smoorenburg
1972b; Zwicker 1955). The interesting question is whether
propagation of energy through the basilar membrane might
play a role and whether the propagation is unidirectional.
Questions of bidirectional propagation of energy and of
0022-3077/98 $5.00 Copyright q 1998 The American Physiological Society
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Richter, Claus-Peter, Burt N. Evans, Roxanne Edge, and Peter
Dallos. Basilar membrane vibration in the gerbil hemicochlea. J.
Neurophysiol. 79: 2255–2264, 1998. Excised gerbil cochleae were
cut along the mid-modiolar plane (hemicochlea). Along one-half
turn of this preparation, fluorescent microbeads were placed on the
basilar membrane (BM). The BM was vibrated with click stimuli
(50 ms) produced mechanically by a piezo pusher. The stimulus
delivery probe could be positioned either more apical or more basal
from the beads. Vibration patterns were measured with a wide
bandwidth photomultiplier from the movements of the beads. When
the probe was positioned more basal, the responses to click stimuli
were brief, damped sinusoids. According to the fast Fourier transforms (FFTs) of the averaged time wave forms, the best frequency
between successive beads decreased toward the apex (0.8 octave/
mm). Sharpness of tuning of the normalized FFT spectra (NQ10dB )
on average was 1.5. Response amplitude at a fixed input level,
measured at different beads away from the stimulation site, dropped
exponentially (58 dB/mm). In addition, for each individual bead,
amplitude dropped linearly with decreasing stimulus intensity. In
experiments where the stimulating probe was placed more apical,
two major properties were observed: first, beads revealed only the
spectral components present in the motion of the probe. Second,
magnitude reduction of the displacement of the cochlear partition
was greater, on average 155 dB/mm, indicating a lack of significant
propagation in the reverse direction.
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C.-P. RICHTER, B. N. EVANS, R. EDGE, AND P. DALLOS
METHODS
Hemicochlea
For a detailed description for the method refer to Edge et al.
(R. M. Edge, B. N. Evans, M. Pearce, C.-P. Richter, X. Hu, and
P. Dallos, unpublished data). The method is reviewed briefly as
follows. After an intraperitoneal injection of a lethal dose of pentobarbital sodium (150 mg/kg), gerbils (Meriones unguiculatus; of
age 18 days-2 mo) were killed. After decapitation, the head was
divided in the medial plane with a razor blade and the bullae were
removed. The bulla was opened and the cochlea was exposed in
balanced Hank’s salt solution (HBSS). After fixation of the bony
inner ear with acrylic to a screw attached to a ball-joint manipulator, the cochlea was cut along the modiolar axis into two parts.
One of the resulting hemicochleae was used for the experiments.
Experimental procedures were approved by the National Institutes
of Health and by the Northwestern University Institutional Review
Board.
On the basis of histological reconstructions of the cochleae, the
distances of the cut edges from the basal end of the basilar membrane were estimated. By adding the length between the beads and
the cut edges of the hemicochleae to the distance of the cut edges
from the base, a distance measure for the beads from the basal end
of the cochlea was obtained. The span between the cut edges and
the beads was determined through the microscope. Thus it was
possible to estimate the corresponding in vivo best frequencies for
the cut edges and beads according to the published frequency-place
maps for the gerbil (Echteler et al. 1989; Müller 1996; Schmiedt
and Zwislocki 1977).
Fluorescent beads
Fluorescent beads of diameters 6, 10, 20, and 90 mm were purchased from Polyscience (Warrington, PA). Single beads were
picked up with a micropipette by application of gentle suction to
the pipette. After the micropipette was close to the bead’s destined
place, suction was released and the bead detached from the electrode and deposited onto the basilar membrane (Fig. 1).
Experimental setup
The experimental setup consisted of an upright Leitz microscope
(Leitz, Ergolux AMC) equipped with fluorescent epi-illumination
and a dual port viewing head. Light emitted from a mercury lamp
(Leitz/HBO 100 W ultra-high–pressure mercury lamp) was used
to illuminate the fluorescent beads via the epi-illuminator. The
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excitation wavelength for the beads was 511 nm, the emission
wavelength 538 nm. Pictures of the preparation on the microscope
stage could be taken with a cooled CCD color camera (Optronics,
DEI-470) through one port of the viewing head. A photomultiplier
(Leitz, MPV compact) was used to measure the intensity of the
light emitted by the fluorescent beads. The optical field was limited
by a rectangular aperture of approximately the size of the beads.
The aperture could be rear-projected onto the specimen plane. The
signal measured by the photomultiplier was proportional to the
distance by which the fluorescent beads moved in and out of the
aperture of the photomultiplier.
For testing the photomultiplier, a calibration pipette with a fluorescent bead glued to its tip was mounted to a piezo pusher (PZL
007, Burleigh) and was placed on the microscope stage. The displacement of the pipette was parallel to the optical plane.
During the experiments, the hemicochleae were attached to a
ball-joint manipulator. The ball-joint manipulator then was transferred into a stable metal hemisphere filled with HBSS and placed
into a hole on the microscope stage. Initially the surface of the
metal hemisphere and the surface of the microscope stage were
parallel. The cochlea on the ball joint manipulator then was oriented so that the basilar membrane was parallel to the optical axis
and perpendicular to the surface of the microscope stage (radial
view). The ball-joint manipulator then was fixed tightly with a set
screw. This, however, did not allow monitoring the vibration patterns of the beads except at the cut edge of the hemicochlea and
necessitated reorientation for beads further away from the cut edge.
Final adjustments in orientation of the preparation were achieved
by tilting the metal hemishell. The hemishell was angled such that
beads close to the probe and beads further in were visualized at
the same time (Fig. 2). An imaginary line perpendicular to the
surface of the basilar membrane and parallel to the surface of the
hemishell was used to determine the angle for the trigonometric
correction. The angle b was measured between the surface of the
microscope stage and the surface of the hemishell. Then a Å
p /2 0 b (Fig. 2). Trigonometric corrections were made to obtain
the transverse component of basilar membrane vibration c from
the measured oblique motion of the beads relative to the optical
axis of the microscope a; c Å a/sin a. Rotation around the optical
axis was minimal and was not considered in the corrections. Once
the preparation was oriented, the stimulation probe was brought to
the basilar membrane until the bead at the tip of the glass pipette
contacted the subsurface of the basilar membrane (facing scala
tympani). The basilar membrane reflected the light emitted from
the fluorescent bead at the tip of the electrode. Thus contact of the
probe to the basilar membrane could be detected easily by visual
inspection while advancing the probe. The angle of the stimulation
probe was almost perpendicular to the subsurface of the basilar
membrane in the experiments.
For measurements, the aperture of the photomultiplier was
placed over half of the surface image of the beads. Transverse
motion of the basilar membrane lead to maximum light intensity
change by the bead moving in and out of the aperture. Positioning
was achieved by moving the entire microscope stage in the optical
plane. The orientation of the slit then could be optimized by rotation
of the photomultiplier around the optical axis.
Photomultiplier
Frequency response properties and sensitivity of the system
were determined respectively with a light emission diode ( LED )
and a fluorescent bead ( 90 mm diam) attached to the tip of a
micropipette. The micropipette was fixed to a piezo pusher ( PZL
007, Burleigh ) and could be displaced by known amounts ( between 2 nm and 5 mm) .
FREQUENCY RESPONSE PROPERTIES. A red LED was focused on
the photomultiplier using the upright Leitz microscope. The signal
for the LED was forward biased by a DC voltage of 2.5 V and
modulated by a ternary noise stimulus (100-mV peak).
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longitudinal coupling in the basilar membrane are addressed
in the present experiments. A suitable preparation for these
investigations is the ‘‘hemicochlea.’’ A cochlea, cut in two
along the mid-modiolar plane (Hu et al. 1995), allows access
to the basilar membrane at the more basal or more apical
cut edges of an individual half-turn. Fluorescent spheres,
located along a half-turn of the hemicochlea, can be used to
evaluate response properties at different locations along the
basilar membrane while the latter is driven mechanically
either at a more basal or more apical site. The advantage of
the preparation, in comparison with in vivo measurements,
is the possibility of evaluating the propagation of energy
along the basilar membrane in two directions, from base to
apex and vice versa. Furthermore, it is possible to obtain
measures of vibratory patterns at several locations in the
same preparation. The drop in response amplitude of the
different beads with increasing distance from the stimulation
probe serves as a measure of longitudinal coupling.
BASILAR MEMBRANE MECHANICS IN HEMICOCHLEA
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FIG . 1. Video view of one turn of a
hemicochlea. A fluorescent bead ( Ç20 mm)
is located on the basilar membrane with a
photomontage.
the sequence (i.e., the 2nd half of the waveform was the same as
the 1st one but of the opposite sign). For the frequency range
(0.13–22 kHz), no drop in magnitude (Fig. 3A) and no phase
shift of the response signal could be detected (Fig. 3B). This
indicates flat frequency response behavior of the measuring system,
at least °22 kHz. The corner frequency of the measuring system
was determined by the rise-time of the response of the photomultiplier to a voltage step applied to the LED. The time to reach 63%
of the maximum response was 1.5 ms which corresponds to a corner
frequency of Ç106 kHz.
MINIMUM DETECTABLE RESPONSE AND LINEARITY. The amplitude of the photomultiplier response to a sinusoidal movement
(100 Hz) of the fluorescent bead decreased linearly down to ¢10
nm with decreasing motion of the bead (Fig. 4).
Stimulus
A micropipette with a 90-mm fluorescent bead attached to its tip
with acrylic was mounted on a piezo stepper (PZL 007, Burleigh)
and used to deliver mechanical stimuli almost perpendicular to the
plane of the basilar membrane. A micromanipulator was used to
advance the piezo and the stimulation probe to the basilar membrane until mechanical contact was observed. Subsequently, during
the experiments, the basilar membrane was moved by mechanical
pulses of the probe toward scala vestibuli. Time waveform of the
displacement for one probe, loaded by the basilar membrane, is
shown in Fig. 8A. The corresponding frequency spectrum is plotted
in Fig. 8B. The maximal amplitude of the probe movement when
electrical square pulses (50 ms, 1–3 V) were applied to the pusher
was between 0.4 and 1.2 mm.
FIG . 2. Sketch shows the basilar membrane with a bead placed onto it.
Preparation is angled to visualize beads that are further in from the cut
edge. First, the basilar membrane is aligned at the cut edge to be parallel
to the optical axis ( a Å 907 ). After further tilting of the preparation, the
basilar membrane is no longer parallel to the optical axis. The angle between
basilar membrane and optical axis is p /2 0 a. Size of the actual movements
detected by the photomultiplier (PTM) thus are reduced and require correction. Actual amplitudes of the bead’s movement c is the movement measured
by the PTM, a divided by sin a.
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Data analysis
Responses measured by the photomultiplier were fed into an
anti-aliasing Bessel filter (corner frequency 20–30 kHz). Subsequently, the filtered response was sampled by a DAS50 board at
a sampling rate of 1 MHz. Off-line analysis included visual inspection of the time waveforms and determination of frequency response using a FFT of the analogue signal. The FFTs were normal-
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The response of the photomultiplier to the stimulus was measured to determine magnitude and phase properties of the system.
A pseudorandom ternary noise sequence with a flat magnitude, and
zero phase response up to roughly half of the sampling rate of 90
kHz (Møller 1981; Zierler 1959) was generated via a programmable waveform generating board (Metrabyte, AWFG-2). The ternary noise used here was generated with three amplitude levels
( 0a, 0, a) and a recursive algorithm with memory (n Å 6), resulting in 728 (or 3 n 0 1) amplitude level transitions per period.
The fast Fourier transform (FFT) was performed with 728 points
and resulted in n Å 182 nonzero odd frequency components. The
(182) even frequency components were zero, reflecting the odd
(inverse-repeat) character of the waveform around the middle of
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C.-P. RICHTER, B. N. EVANS, R. EDGE, AND P. DALLOS
ized to their maximum amplitude. The frequency of the maximum
of the ratio between beads’ FFT and probe’s FFT was designated
the ‘‘best frequency.’’ To measure the bandwidth of the obtained
FFT spectra, a normalized sharpness (NQ10dB ) has been defined
(best frequency of the FFT spectrum/bandwidth of the normalized
FFT spectrum at a magnitude of 0.32 peak).
The logarithmic decrement q of the vibration patterns of the
cochlear partition was calculated as described by von Békésy
(1960, page 458): q Å ln (i 2 /i 1 ), where i 2 /i 1 denotes the amplitude
ratio between successive response cycles.
RESULTS
These experiments were performed to study basic mechanical vibration properties of the BM. Therefore, mechanical pulse stimuli were applied directly to the BM in 22
hemicochleae. Responses to such stimuli were used to determine filter properties and damping of the BM vibration at
different locations along a hemiturn. The stimulus probe was
placed either at the basal cut edge (n Å 17; cut edge closer
to the basal end of the cochlea) or the apical cut edge (n Å
9; cut edge closer to the apical end of the cochlea). Thus
energy propagation and drop in response magnitude could
be studied in two directions.
Reliability of measurements
DATA ACQUISITION. As described in METHODS, both bullae
were removed after killing the animals and the cochleae
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FIG . 4. Response properties of the photomultiplier measuring system to
the motion of a fluorescent bead mounted on a piezo pusher (PLZ007,
Burleigh). Sinusoidal bead movements (frequency of 100 Hz) of different
amplitude were measured. Linear decrease of the measured magnitude down
to Ç10 nm was obtained.
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FIG . 3. Response properties of the photomultiplier measuring apparatus.
Magnitude-frequency plot of the responses to an iso-intensity light stimulus
from a light emission diode (LED; A). Corresponding phase plot (B).
Response properties show flat frequency response for the measuring system
at least °22 kHz.
were exposed and cut in the mid-modiolar plane. These procedures took Ç30 min. Thereafter, fluorescent beads were
placed on the basilar membrane at different locations along
a half-turn. The placing of the beads, the positioning of the
preparation on the microscope stage and the placing of the
probe to vibrate the basilar membrane took on average 154
min (range: 30–390 min; standard deviation: 39 min). After
the hemicochleae were placed, the data were acquired within
an average time interval of 75 min (range: 16–151 min;
standard deviation: 12 min).
REPEATED MEASUREMENTS. Repeated measurements which
were done within the time interval of 1 h did not show
changes in the best frequency. However, there was variation
in the amplitude obtained (Fig. 5). Here two examples are
shown, HCoRev1 and HCoRev2. They revealed a scatter in
peak-to-peak amplitude of 0.48 { 0.16 mm [characteristic
frequency (CF) changed from 2,750 to 2,500 Hz, which
equals 0.14 octaves] and 0.36 { 0.06 mm (no CF change
was detected). Examples of FFTs of the time waveforms
are shown in Fig. 5. In example HCoRev1, the amplitude
decreased after the first trial but then remained almost constant. However, in HcoRev2, the amplitude was initially
constant but the last trial showed an increase. One reason for
the observed changes in amplitude might be due to possible
changes in light intensity from the mercury lamp used to
excite the fluorescent light. Despite the scatter in amplitude
found in repetitive measurements, the results did not show
a systematic increase or decrease in vibration amplitudes.
VARIABLE LOAD OF THE BASILAR MEMBRANE. In three experiments, the influence of a change in the load on the
vibration probe by the basilar membrane was tested. For
this purpose, the location of the probe, which initially was
positioned by eye, was changed by altering the DC voltage
to the piezo pusher. Thus the position was changed {1.5
mm relative to the initial position. Increasing the tension
of the basilar membrane slightly increased the vibration
amplitude, whereas retraction of the probe decreased the
vibration amplitude at an approximate rate of 0.6 dB / mm
BASILAR MEMBRANE MECHANICS IN HEMICOCHLEA
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FIG . 5. Fast Fourier transforms (FFTs) of the responses obtained from
fluorescent beads when the basilar membrane was vibrated mechanically
by a probe. Two examples were obtained from the 1st turns of 2 different
cochlear preparations (HCoRev1 and HCoRev2). Frequency of maxima of
the plots is not changing significantly within the time interval. At best
frequency, amplitudes of the responses are not systematically increasing or
decreasing. Note, in HCoRev1 a decrease occurs after the 1st trial, followed
by nonsystematic changes. However, in HcoRev2, an increase occurs at the
end of the measurements.
( Fig. 6, right ) . Detaching of the probe from the basilar
membrane resulted in a further decrease in vibration amplitude ( Fig. 6, left ) . This drop could be measured at any
of the beads located along the hemiturn. The frequency
spectrum of the vibration was not affected by different
loads to the basilar membrane.
Stimulus is basal to site of measurement
Examples of time responses and FFTs are shown for three
preparations in Figs. 7 and 8. Impulse responses appeared
as brief, filtered damped sinusoids. The frequency of this
sinusoid was specific to a given fluorescent bead’s location.
The time waveforms obtained from different beads revealed
a decrease in frequency of the oscillations with increasing
distance of the beads from the stimulation probe (Figs. 7A
and 8A). Corresponding FFTs showed that the vibration
pattern at any bead was tuned, reflecting a distinct best frequency (Figs. 7B and 8B). According to the FFTs of the
time waveforms, the shift in best frequency between successive beads was between 0.3 and 1.7 octaves/mm, on average
0.8 octave/mm (n Å 20). A slight, nonsignificant decrease
of the CF-shift was found with increasing distance from the
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FIG . 6. After the stimulation probe was placed against the basilar membrane under visual control, the probe’s position was varied, and the corresponding vibration amplitude was monitored. Increasing the load on the
basilar membrane (positive numbers, right) slightly increased the vibration
amplitude, whereas small retraction of the probe (negative numbers, right)
from the basilar membrane led to decreased vibration amplitude as measured
by the movements of the beads located on the basilar membrane. Detaching
of the probe from the basilar membrane further decreased the vibration
amplitude (left). When the probe is further withdrawn from the BM but
still immersed in scala tympani, vibration amplitude further decreased. For
the latter case, the energy required to vibrate the basilar membrane is
transmitted through the fluids.
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base. The NQ10dB of the obtained response curve was between 0.6 and 2.7, on average 1.5. A small, nonsignificant
decrease in NQ10dB was attained with increasing distance
from the base of the BM ( n Å 32). Response amplitudes to
stimuli of different intensities obtained from individual
beads dropped linearly (Fig. 9).
Reduction between successive peaks of a given sinusoidal
response was measured and the logarithmic decrement ( q)
was computed. q was between 0.16 and 1.8, on average 0.6
(n Å 30). The decay of the amplitude at different beads
away from the stimulation location could be described as an
exponential drop of Ç58 dB/mm (Fig. 11A).
To determine whether energy is mainly propagated via
the fluids or the BM, a hole was made into the arcuate zone
(between stimulus delivery and measurement sites) using a
glass pipette. If energy is propagated by the BM, this ‘‘cutting’’ of the BM should decrease the vibration amplitude
significantly. This manipulation lead to an immediate drop
of the response amplitude by 7.8 dB beyond the cut. A bigger
decrease in response magnitude is expected if pectinate zone
and tectorial membrane could be separated as well. FFT
spectra of the sinusoidal responses showed the same frequency distribution before and after the cut of the basilar
membrane. Only the magnitude of the FFT spectra decreased.
Interestingly, beads placed in four hemicochleae revealed
no tuning. Aside from magnitude scaling, time waveforms
and FFTs at the different beads were essentially identical to
the responses obtained from the stimulation probe. For these
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cochleae, the drop in magnitude of the bead movement was
19 dB/mm for iso-intensity stimuli (Fig. 11C).
FIG . 8. A: example of nonnormalized time waveforms obtained at beads
located in the 1st turn of a gerbil hemicochlea (preparation HCo112).
Distances are from the basal end of the cochlea. B: FFTs of the time
waveforms shown in A.
showed a reduction of response amplitude of 15 dB/mm
(Fig. 11C) with increasing distance from the probe. This is
in reasonable agreement with responses from beads obtained
in the hemicochlea which did not show tuning (19 dB/mm).
Therefore, for the latter cochleae, it is surmised that the
beads were only loosely attached to the basilar membrane
and did not reflect its vibratory properties.
Stimulus more apical to site of measurement
Time waveforms obtained from 26 different beads placed
in nine different cochleae reflected the properties of the stimulation probe. A shift in frequency of the oscillations with
increasing distance of the beads from the stimulation probe
was not observed (Fig. 10). The reduction of the amplitude
was on average 155 dB/mm (Fig. 11B).
Beads in a glass tube
Experiments to mimic fluid properties in the hemicochlea
in the basal turn were carried out. Beads were placed in a
glass tube (length: 3 mm; diameter: 0.68 mm) and immersed
in a dish of HBSS. A probe similar to that used in the
hemicochlea experiments was placed in front of the opening
of one end of the glass tube. Again, electrical square pulse
stimuli were applied to the piezo pusher. A mechanical click
response was produced by the stimulus delivery probe. The
beads located along the longitudinal axis of the glass tube
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FIG . 9. Stimulus intensity vs. vibration amplitude measured at several
beads. Data for 5 representative preparations are shown. Thick line represents linear response.
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FIG . 7. A: normalized time waveforms obtained at beads located in the
1st turn (preparation HCo116) and 2nd turn (preparation HCo142) of 2
different gerbil hemicochleae. Distances are from the basal end of the
cochlea. Distance of the probe from the basal end of the basilar membrane
was 3.5 mm (HCo116) and 7.6 mm (HCo142). B: FFTs of the time
waveforms shown in A. Magnitudes are normalized to the maximum value.
Response curves showed a NQ10dB of 1.0, 1.5, 1.5, and 1.2 (from left to
right). An orderly shift of the maxima of the magnitude plots occurs with
lower frequencies corresponding to more distal points.
BASILAR MEMBRANE MECHANICS IN HEMICOCHLEA
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FIG . 10. Time waveforms (A) and corresponding FFT spectra at beads
located in the 1st turn when the stimulation probe was placed more apical
to the measuring site. For these experiments, energy propagation from the
apex to the base was studied. Spectral response properties obtained at all
beads reflected that of the stimulation probe. Drop in vibration amplitude
for this preparation was Ç140 dB/mm, but interestingly Ç190 dB/mm
from probe to 1st bead.
DISCUSSION
Overview
Experiments in the hemicochlea revealed some of the
passive mechanical properties of the gerbil inner ear. Direct mechanical vibration of the BM with mechanical pulse
inputs showed band-pass responses for different beads located along the BM. The responses to broadband stimuli
were brief highly damped sinusoidal waveforms with different frequencies. Normalized sharpness of the response
curves ( NQ10dB , on average 1.5 ) , shift in best frequency
( on average 0.8 mm/ octave ) , and logarithmic decrement
( on average 0.6 ) were determined from the responses.
From cochleae in poor condition or from in vitro cochlear
preparations, similar results have been obtained by others
[ guinea pig : best frequency: 0.8 kHz, NQ10dB : 0.94 )
( Rhode 1973 ) ; squirrel monkey: best frequency: 8 kHz,
NQ10dB : 1.4 ( Rhode and Robles 1974 ) ; guinea pig : best
frequency: 8 kHz, NQ10dB : 0.94 ( Rhode and Cooper 1993 ) ;
chinchilla: best frequency: 10 kHz, NQ10dB : 1.8 – 2.0 ( Ruggero et al. 1992 ) ] . Thus aspects of the present findings
coincide with the results of other groups, reflecting the
operation of the passive cochlea. However, the logarithmic
decrement q was better in the present set of data ( 0.6 ) than
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FIG . 11. Drop in peak to peak amplitude of the time waveforms vs.
distances of the beads from the stimulation probe. A–C: each data point
represents 1 bead used for measurements, each type of symbol represents
1 preparation. A: stimulus probe was located at the more basal cut edge of
the hemicochlea. B: probe was located more apical. For the symbols with
a downward arrow, no response could be measured. Each point with a
downward arrow shows the noise amplitude obtained at the beads’ location.
C: small symbols represent beads that only reflected the spectral properties
of the stimulation probe (thick line). Large open diamonds show beads in
a glass tube (thin broken line).
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that found by von Békésy, between 1.4 and 1.8. Ruggero et
al. ( 1992 ) showed a q of Ç0.09 in a living animal and a
q of Ç0.5 post mortem and at high sound pressure levels.
Because the logarithmic decrement increases with post
mortem time, the q might be a measure for assessing the
condition of the preparation.
A frequency place map for the hemicochlea has been developed using the FFT results of the bead responses and the
distances of the beads from the basal end of the basilar
membrane (Fig. 12). Compared with in vivo frequency
place maps based on horseradish peroxidase (HRP) staining
of single fibers with determined CF of adult animals (Echteler et al. 1989; Müller 1996), the frequency place map
in the hemicochlea was shifted Ç1.4 octaves toward lower
frequencies. According to the literature, the frequency place
map in a dead cochlea shifts Ç0.5–0.9 octaves (Rhode
1973; Rhode and Robles 1974; Ruggero et al. 1992). These
data were obtained within the first hour after death. However,
a decrease in the characteristic frequency as a function of
time after death has been described in BM vibration amplitudes (Rhode 1973; Rhode and Robles 1974) with a shift
2262
C.-P. RICHTER, B. N. EVANS, R. EDGE, AND P. DALLOS
of Ç1.4 octaves toward lower frequencies. In the present
experiments, the mean shift of 1.4 octaves of the BM frequency place map, then might be explained by the times
after death for the measurements, which were usually 3.0 h
(range: 1.0–6.5 h) after killing the animal. The scatter of
the data presented for one location (same distance of the
bead from the basal end of the basilar membrane) also may
be caused by the differing times between killing the animal
and data acquisition.
For an isolated preparation, the cochlear amplifier is probably not active. In the present experiments, a linear magnitude response versus stimulus intensity was found (Fig. 9).
Therefore the nonlinear behavior of basilar membrane vibration patterns is missing. This finding is in agreement with
cochleae in poor condition or excised cochleae (Khanna
and Leonard 1986; Rhode and Robles 1974; Ruggero et al.
1992).
Direction of energy propagation
In the present preparation, propagation of energy on the
basilar membrane from base toward apex and vice versa
could be investigated. As shown, tuned BM vibration patterns were observed if the basilar membrane was stimulated more basal than the location the vibration of which
was measured by the behavior of the beads. In none of
our experiments could we detect a tuned vibration pattern
of the BM if energy propagated from the apex to the base.
The question, whether a traveling wave from apex to base
is sustainable in the cochlea was addressed by von Békésy
( 1928 ) . He moved the stapes to more apical positions in
the cochlea, but he never saw a traveling wave running
from apex to base. However, in his experiments, he investigated the whole cochlea, including at least the fluids and
the basilar membrane properties. The acoustic energy in
his experiments was coupled to the basilar membrane
through the fluids. No matter where introduced, this acoustic energy propagates in the scalae with the speed of sound
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FIG . 12. Frequency-place map obtained from the beads measured in the
hemicochlea [h , 11.2 mm Å 100%] in comparison with the in vivo frequency place map published by Müller (1996) [thick line; animals with
age of 2–4 mo; 11.1 mm Å 100%], Schmiedt and Zwislocki (1977) [thin
line; 12.1 mm Å 100%] and data point obtained by Echteler et al. (1989)
( ∗ ).
and thus provides an essentially instantaneous pressure
gradient across the basilar membrane. This pressure gradient sets the membrane in motion and a well-behaved traveling wave results as an aftereffect. Direct experimental
investigation of wave travel for the case when energy is
directly conveyed to the basilar membrane has been lacking. Thus potential reverse propagation properties only
have been investigated partially. In the present experiments, based on direct mechanical input, no locally tuned
vibration of the BM could be observed if energy propagated toward the base of the basilar membrane. As a consequence, one may surmise that in the case of otacoustic
emissions of any sort, direct propagation of energy
through the basilar membrane seems unlikely. Local
sources of vibration on the basilar membrane could probably couple directly into the scala vestibuli fluids and the
resulting pressure would drive the stapes footplate. Delay
times for evoked otoacoustic emissions of ú10 ms ( for
review see Probst et al. 1991 ) remain unexplained, inasmuch as they cannot incorporate a ‘‘reverse traveling
wave’’ time delay.
The situation that energy has to be somehow propagate
from apex to base in the cochlea might be similar for distortion products. In this case, two tones of frequency f1 and f2
(f1 õ f2 ) are applied simultaneously to the ear, generating
intermodulation distortion (colloquially called combination
tones), including f2-f1 , 2f1-f2 , and 2f2-f1 (for a historical
review, see Goldstein and Kiang 1968; Plomp 1965;
Smoorenburg 1972a). The component 2f1-f2 is audible in a
restricted frequency region below f1 (Goldstein 1967; Plomp
1965; Smoorenburg 1972a; Zwicker 1955), and it is highly
dependent on the frequency separation of f1 and f2 (Goldstein
1967). There is experimental evidence that combination
tones are generated at one place on the basilar membrane and
propagate to the basilar membrane site with characteristic
frequency equal to that of the combination tone (Goldstein
1967; Siegel et al. 1982; Smoorenburg 1972b; Zurek and
Sachs 1979). Such an origin is consistent with the presence
of combination tones in recordings of cochlear microphonics
(Gibian and Kim 1982), responses of cochlear nerve fibers
(Buunen and Rhode 1978; Goldstein and Kiang 1968; Kim
et al. 1980; Siegel et al 1982), and basilar membrane measurements (Nuttal et al. 1990; Rhode and Cooper 1993;
Robles et al 1990). In these cases, judging from the present
set of data, the dominant coupling of energy is through the
fluids and not via the basilar membrane. The findings of the
present experiments showed a drop in vibration amplitude
of 155 dB/mm from an apex to base direction. Thus propagation of energy through the basilar membrane from apex to
base is unlikely. Interestingly, and in harmony with the
above, in a simple transmission line model it has not been
possible to set up a traveling wave running in the direction
of high to low compliance.
In four of the cochleae, no tuned response properties at
the different beads were obtained. For these cochleae, the
drop in response amplitude of the beads with increasing span
from the vibration probe was similar to the drop in response
amplitude of beads placed in a glass tube. The suggestion
is that these beads were not attached to the basilar membrane
and therefore did not reveal its vibration properties. Rather,
the beads were attached loosely or floating, reflecting the
BASILAR MEMBRANE MECHANICS IN HEMICOCHLEA
We thank Dr. M. A. Cheatham for discussions and comments on the
manuscript.
This work was supported by National Institute of Deafness and Other
Communications Disorders Grant DC-00708 and Deutsche Forschungsgemeinschaft Grant Ri 699/5–1.
/ 9k28$$my06 J380-7
Address for reprint requests: C.-P. Richter, Northwestern University,
Frances Searle Building, 2299 North Campus Dr., Evanston, Il 60208.
Received 8 May 1997; accepted in final form 8 January 1998.
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vibration patterns of the stimulation probe transmitted by
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