The size and shape of intracochlear pressure

1
The size and shape of intracochlear pressure and
its use in the study of cochlear mechanics.
Elizabeth (Lisa) Olson Fowler Memorial
Laboratory OTO/HNS and Biomedical
Engineering Columbia University, New York
2
Audible sound pressure amplitudes and frequencies
Reference From Sound to Synapse by C.D.Geisler,
Oxford University Press, 1998.
3
The outer and middle ear transmit the sound
energy to the inner ear.
Stapes
Inner ear
4
Because of the the middle and outer ears, at
frequencies where they are most effective, all
the sound energy passing through a 1cm2 area is
absorbed in the inner ear. From Rosowski et
al., By comparing Power flow area x pressure
velocity at the ear canal and at the stapes.
5
The impedance of air, (P/velocity) is 415 Pa /
m/s (resistive). The input impedance of the
cochlea (P/velocity at the stapes) is 105 Pa /
m/s (also resistive, due to cochlear traveling
wave).
6
The middle ear is often thought of as a lever.
7
The force on the eardrum is transmitted via the
ossicles to the much smaller oval window. The
pressure at the stapes is increased by a factor
of A/a.
Drawing adapted from From Sound to Synapse by
C.D.Geisler, Oxford Univ.Press, 1998
8
The malleus and incus form a lever, L/l.
L
l
9
This simple leveraging model of the middle ear
has the eardrum moving as a rigid piston, and the
pressure transmitted to the inner ear instantly.
10
This simple leveraging model of the middle ear
has the eardrum moving as a rigid piston, and the
pressure transmitted to the inner ear instantly.
11

• Although the factor of 50 is not too far off
  (pressure at stapes / pressure in earcanal 30
  in gerbil) ..
• other observations are not consistent with the
  simple leveraging model.
• The pressure at the cochlea is delayed relative
  to the pressure in the ear canal.

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Pressure sensor
Sensor tip
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Measurements of scala vestibuli pressure and ear
canal pressure
tone
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GERBIL Intracochlear responses to ear canal
pressures of 80 dB SPL. Basic result Most
frequencies transmitted equally well. Gain is
30 dB. Phase is straight line (such as a
constant delay would give.)
15
Phase is straight line (such as a constant delay
would give.)
From slope 1 cycle in 40 kHz, so delay 25 ms.
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Measurements of scala vestibuli pressure and ear
canal pressure
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RESULTS - scala vestibuli pressure was nearly
identical to ear canal pressure, increased by a
factor of 30. - The scala vestibuli pressure
was DELAYED. The transmission delay was 25
microsec.
Delayed 25 ms
18
Here the ear canal pressure plot has been shifted
25 ms.
19

• Observations are not consistent with the simple
  leveraging model.
• The pressure at the cochlea is delayed relative
  to the pressure in the ear canal.

2. Except at frequencies below about 1kHz, the
middle ear does not move as a rigid body,
but as a distributed system.
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Complex Eardrum Vibration
Decraemer and Khanna, 1997
21

• Observations are not consistent with the simple
  leveraging
• model.
• The pressure at the cochlea is delayed relative
  to the pressure in the ear canal.
• Except at frequencies below about 1kHz, the
  middle ear does not move as a rigid body, but as
  a distributed system.

These observations (and others) suggest that the
sound energy is transmitted through the middle
ear as a mechanical wave.
The physical basis for this middle ear wave is an
active research question.
22
Inner ear
23
cochlea
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Guinea pig cochlea
outer shell removed
The cochlea has a coiled structure.
Cross-section of gerbil cochlea
25
2 mm
Cross-section of gerbil cochlea
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Organ of Corti
20 mm
Image Pujol R. Anatomie et physiologie de la
cochlée. Arch Int Phys Bioch , 97-4, 1989
http//www.iurc.montp.inserm.fr/cric/audition/engl
ish/ear/cochlea/corti/fcorti.htm
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Organ of Corti
20 mm
Image Pujol R. Anatomie et physiologie de la
cochlée. Arch Int Phys Bioch , 97-4, 1989
http//www.iurc.montp.inserm.fr/cric/audition/engl
ish/ear/cochlea/corti/fcorti.htm
28
Pujol R. Anatomie et physiologie de la cochlée.
Arch Int Phys Bioch , 97-4, A51-A78,
1989 http//www.iurc.montp.inserm.fr/cric/audition
/english/ear/cochlea/corti/fcorti.htm
29
Endolymph KCl, low Ca High Voltage 80mV
Perilymph NaCl
Special electrical make-up of the cochlea
Transduction how does the mechanical stimulus
get translated into the electrical language of
the brain?
30
Transduction by hair cells Motion of the organ
of Corti causes stereocilia to tilt. This opens
ion channels, allowing ions to flow into the
hair cells. This leads to intracellular voltage
changes and transmitter release.
OHC
IHC
Note IHCs and OHCs play very different roles in
hearing.
http//www.iurc.montp.inserm.fr/cric/audition/engl
ish/ear/cochlea/corti/fcorti.htm And page of D.
Freeman, MIT.
31
Using widely opened cochleae and very high
stimulus levels, von Bekesy observed that the
organ of Cortis motion was like a traveling
wave. The physical basis for the wave is the
interaction between the mass of the cochlear
fluid and the stiffness of the organ of Corti and
basilar membrane.
Békésy (1941)
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Chamber depth 1mm Normal wave height ltlt 1mm
Cochlear traveling wave Simulation of organ of
Corti motion from Steven Neely. Note that as the
stimulus frequency decreases the peak of the
response shifts further towards the apex of the
cochlea.
33
Howard Hughes Medical Institute Movie (available
on their web page and courtesy of HHMI and Jim
Hudspeth, Rockefeller University)
34
Physical mechanism for tonotopic
(place-dependent) tuning
Early models of cochlear tuning likened the organ
of Corti to a set of separately tuned spring-mass
resonators like strings on a musical
instrument.
35
Longitudinally decreasing stiffness is important
for all models of tonotopic tuning.
(1) Going from base to apex, basilar membrane
gets wider.
(2) Going from base to apex, OHCs get longer.
(3) Going from base to apex, stereocilia get
longer. (4) gtgtgt Going from base to apex,
structures get less stiff.
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Amplitude of motion divided by amplitude of
stimulus pressure
Modern measurements of basilar membrane motion in
healthy cochleae showed that with sound
frequencies close to a places best frequency the
b.m. motion did not scale linearly with sound
level. The result was enhanced tuning and an
enlarged dynamic range.
Phase of motion, referenced to stimulus pressure
Data from Ruggero et al., JASA 1012151-2163
(1997)
37
Nonlinearity allows the ear to be sensitive to a
wide range of stimulus levels, given a relatively
small operating range at the detector (hair cell).
38
What displacements do these velocities correspond
to?
A displacement of 1 nm is the threshold of
hearing smaller displacements are in the
noise. At displacements greater than 500 nm
the auditory sensory cells will begin to be
damaged.
39
(No Transcript)
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What gives rise to the sharp tuning and
nonlinearity?
Nonlinearity disappears.
41
How?
Somatic motility? Stereocilia motility?
42
Figure modified from deBoer, JASA 98, 1995.
The design of an experiment to measure the
outer hair cell force Consider force-balance
on a longitudinal segment of the organ of Corti
(ie, force/length). The forces are
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Passive restoring and resistive forces at
attachment points (eg, Fpassive -kx Rv)
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b
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Force due to OHC pushing against support
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m
F (Psv Pst ) b Fpassive Fohc ma
F (Psv Pst ) b - kx -Rv Fohc ma
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(Psv Pst ) Fohc ma - Fpassive
In a linear system this would be Zpassive v,
where Zpassive is the impedance of the OC and v
is the vertical velocity of the basilar membrane.
(Zpassive represents the stiffness, resistance
and mass of the OC.) ma - Fpassive ma kx
Rv (miw ik/w R)v
Zpassive
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(Psv Pst ) Fohc Zpassive v
To get at Fohc, would like to measure fluid
pressure close to the organ of Corti both above
and below, and the velocity of the basilar
membrane over a range of sound pressure levels.
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Pressure was measured in-vivo in the base of the
gerbil cochlea.
and in scala vestibuli near the stapes.
50
Basic observations of the pressure
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Basic observation 1 The pressure in scala
tympani close to the basilar membrane is tuned
and nonlinear
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velocity
pressure
40 dB SPL stim.
85 dB SPL
In fact, the tuning and nonlinearity of the
pressure close to the basilar membrane is quite
similar to the velocity of the basilar membrane
measured by Ruggero et al. (and others).
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Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
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Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
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Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
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Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
57
Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
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Basic observation 2 The pressure in scala
tympani close to the basilar membrane is rapidly
varying in space
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This experimental result confirmed the model
prediction that in the region of the peak the
pressure variations would be localized close to
the organ of Corti. (Simulation from Lloyd
Watts.)
Next slide a closer look at some of the details
of the spatial variations, and their
significance.
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Scala tympani pressure at various distances from
the basilar membrane
Large pressure gradients large fluid motion
large BM motion (close to best frequency).
Small pressure gradient small fluid motion, but
still robust pressure.
Rapid phase-frequency variation pressure that
is delayed with respect to pressure at stapes
(traveling wave).
Flat phase-frequency variation pressure that is
in-phase with pressure at stapes (not traveling
wave).
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These characteristics were predicted by the
fast-symmetric-wave / slow- anti-symmetric-wave
description of intracochlear pressure proposed in
1950.
stapes
II. Peterson and Bogart recast the pressures and
fluid motions in terms of symmetric () and anti
symmetric (-) parts,
PB recast these
round window
I. Pressures and fluid motions in each chamber
were related using conservation of mass and fluid
force laws.
giving rise to two new equations describing these
two modes
Scala vestibuli
Scala tympani
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stapes
PB recast these
round window
Symmetric part is sound wave moving at speed c
(speed of sound in water). This is a nearly
spatially invariant compression pressure (fast
wave) due to small size of cochlea and large
size of c.
Anti-symmetric part is a wave moving at speed
that is based on fluid density and organ of Corti
basilar membrane mechanical impedance
(especially stiffness). This is the slow wave.
Can neglect
Both modes are needed to match boundary
conditions at stapes and round window, but only
the anti-symmetric mode causes significant organ
of Corti motion.
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Scala tympani pressure at various distances from
the basilar membrane
Large pressure gradients large fluid motion
large BM motion (close to best frequency) gtgt SLOW
WAVE MODE
Small pressure gradient small fluid motion, but
still robust pressure gtgt COMPRESSIVE (FAST)
PRESSURE MODE
Rapid phase-frequency variation pressure that
is delayed with respect to pressure at stapes gtgt
SLOW WAVE MODE
Flat phase-frequency variation pressure that is
in-phase with pressure at stapes gtgt COMPRESSIVE
(FAST) MODE
Notches indicate interference between FAST and
SLOW MODES
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now, return to force balance -- using pressure
measurements to probe the cell-based forces.
(This study was of frequencies up to and
including the peak, and is concerned primarily
with the slow traveling pressure mode.)
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(Psv Pst ) Fohc Zpassive v
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Spatial pressure variations can be used to
determine fluid velocity.
Just next to the basilar membrane,
vz of the fluid vz of
the b.m.
pressure variations can be used
to measure b.m. motion.
z
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(Psv Pst ) Fohc Zpassive vbm
Observe DP and v do not scale linearly with the
stimulus level. This nonlinearity is due to
Fohc, which is what we want to measure. Fohc
will be found by the relative degree of nonlinear
scaling of DP and v.
Example from a good data set.
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(Psv Pst ) Fohc Zpassive vbm
define Zactive -Fohc / vbm
(Psv Pst )/vbm Zpassive Zactive
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(Psv Pst )/vbm Zpassive Zactive
The most interesting level-dependent variation
was that the real part of Z was smaller at low
stimulus levels at frequencies a bit lower than
the peak frequency. (The real part could even
be negative, which signifies power injection) at
low stimulus levels.
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(Psv Pst )/vbm Zpassive Zactive
The most robust finding was that the variation in
Z was small compared to its overall size. That
means Zactive is small compared to Zpassive, and

Fohc is small compared with passive forces in the
cochlea.
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Fohc is small compared with passive forces in the
cochlea.
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But then how can it have such a large effect?
Fohc is small compared with passive forces in the
cochlea.
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F (Psv Pst ) b - kx -Rv Fohc ma
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Ff mf a
F
a
Ff Pst b mf a
mf(l)/2
(Psv Pst ) b - kx -Rv Fohc ma
-mf(l)a - kx - Rv Fohc ma
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Ff mf a
F
a
Ff Pst b mf a
mf(l)/2
(Psv Pst ) b - kx -Rv Fohc ma
-mf(l)ma - kx - Rv Fohc 0
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These are the conservative forces that govern the
cochlear traveling wave. They are in balance
(they cancel each other) so the OHC force doesnt
have to be bigger than them individually to be an
important force.
-mf(l)ma - kx - Rv Fohc 0
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Cochlear models agree (eg. Wen and Boahen
(2003)).

• active force / restoring force
• 1/10 gtgt gain 100

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Another very interesting topic is nonlinear
distortion, and Ill touch on it very briefly.
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In a healthy cochlea, harmonic distortion is
present in the intracochlear pressure close to
the sensory tissue. We used it with a cochlear
model to bound the size of the active force.
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Two tone distortion in intracochlear pressure
If linear, spectra just contains two peaks.
Cochlear nonlinearity produces distortion in the
time domain
that corresponds to a family of spectral peaks in
the frequency domain.
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Distortion products can also be detected
radiating out of a healthy ear and are used for
clinical diagnosis of hearing impairment. You
can also hear them..
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DP - demo
f1
f2
2f1-f2
2000
2800
1200
Frequency in Hz
primary tone f1
primary chirp f2
f1 and f2
From M. Mauermann
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Thank you
Acknowledgements
National Institutes of Health National Science
Foundation Emil Capita Foundation
Fowler Memorial Lab, Columbia U. Wei
Dong Ombeline de La Rochefoucauld Stanley
Huang Nneka Eze Shyam Khanna Willem Decraemer