Physics
of cochlea
Principle
Functional
anatomy
The cochlea is one of the parts of the inner ear (which
also comprises the 3 semicircular canals and otoconia systems, see Fig. 1 of Vestibular systems).
It is a spiraled, hollow, conical structure of three mechanically coupled
canals, the scale vestibuli, scala media and scala tympani,and the membrane of Reissner, the basilar membrane (BM), tectorial membrane (TM) and
the organ of Corti with the sensory hair cells (Fig. 1, 2).
Fig. 1
Cochlea oc organ of Corti, sm
scala media, st scala tympani, sv scala vestibule, sg spiral ganglion with the
bipolar cell bodies of the auditory nerve. (After http://147.162.36.50/cochlea/index.htm)
BM is nearly
Fig. 2 Cochlear
transversal view. Corti’s organ is indicated in the gray rectangular structure
in the middle. The hair bundle of IHCs is not connected to TM, but the longest
stereocilia of OHCs do. (Modified from Wikipedia)
As a reaction to vibration of the oval window, TM and
BM (basilar membrane) move up and down. This causes the hairs of the OHCs and
IHCs to vibrate. The mechanical excitation of the IHCs, leads to electrical
excitation which results in IHC receptor potentials that gives rise to action
potentials in the fibres of the auditory part of the VIIIth cranial nerve.
Non-linear
biomechanics and cochlear amplification
Hair
cells convert sounds into receptor potentials when their stereocilia are
deflected. IHCs act as the receptor cell and OHCs can act as a kind of motor
cells for low and moderate sound levels that is their main function. They
respond to variation in potential, and change length at rates unequalled by other
motile cells. The forces generated by OHCs are capable of altering the delicate
biomechanics of the cochlear partition, resulting in increased hearing
sensitivity and frequency selectivity. The OHC electromotility goes far beyond
the description of the cochlea as a simple frequency analyzer. It behaves as an
active non-linear filter. In this view, frequency selectivity arises through
the suppression of adjacent frequencies, a mechanical effect equivalent to
lateral inhibition in neural structures. All these processes are explained by
the interplay between the non-linear hydrodynamic interactions among different
parts of the cochlear partition along the cochlea and the effective non-linear
behaviour of the electromotil OHCs.
Application
Precise
knowledge of the tonotopical organisation of OC is of importance for the
placement of the electrode bundle of a cochlear implant., which is nowadays
experimentally performed with 32 electrodes.
Cochlear implants have routinely been applied more than 125,000 times
(middle of 2008).
More
Info
Non-linear
biomechanics
The
Reissner's membrane can be neglected in determining the stiffness of the
endolymph sac. The major part of the stiffness of the organ of Corti is caused
by BM, the reason why the biomechanics focuses at BM.
A
travelling wave, starting at the oval window, runs along the BM with decreasing
speed of propagation. The amplitude of vibration along BM first increases and
then decreases quickly after reaching it maximum (Fig. 3). The point of maximal
deflection is determined by the sound frequency. High frequencies resonate at a
point near the windows, while low frequencies resonate more closely to the apex
(also called helicotrema). Formerly, it was thought that practically the whole
BM was mechanically stimulated by a pure tone. However, the mechanical properties
of BM change along its length. From the windows with a membrane width of
The
frequency dependency can be compared with that of length and tension of a
violin string. It is denoted as the place theory or the tonotopical arrangement of
frequencies. In this way, the nerve fibres can only be stimulated by a small
frequency band with the most effective frequency, the best frequency, fbest,
in the middle of the band.
The
non-linearity is based on the mechanical coupling via the viscosity of the
endolymph of adjacent segments of OC that act as oscillators. This gives a
significant sharpening of the BM oscillations. Additional strong sharpening is
provided by the active role of OHC cell bodies (see below).
Fig.
3 BM maximal response to a 250 Hz tone
calculated with a model of the non-linear and active cochlear mechanics.
In
Fig. 4, the hair bundles of IHCs and OHCs are deflected by the shear
displacement between the reticular membrane (RL) at the top of the OC and TM. As
a result, the OHC cell bodies lengthen some 10%, driven by its receptor
potential. The small box (in the upper right corner) shows the range of these
displacements with OHC length change. The dot indicates the input-output
relationship; its vertical motion is proportional to the input (BM
displacement) and its horizontal motion is proportional to the output (IHC
displacement). The dot goes beyond the limits of the box of Fig. 4b. As a
result, the oscillatory behaviour of the BM-OHC-TM system is enhanced by the
electrically driven length changes of the OHCs (called electromotility). This behaviour was
established by interferometric (see Interferometry) measurements based on
laser beam reflections from the basilar membrane and RL. Fig. 4b shows the organ of Corti with contracted OHCs. This is
the basis of the OHC amplifier function. The changes in length of OHCs and
Deiter cells enhance the resonance of BM by pumping energy into the mechanical
system in the same way that one does when "pumping a swing". The
energy contributed by OHCs will improve the sensitivity of the cochlea to
low-level sounds, resulting in a larger stimulation of IHCs. This is the basis
for the amplifier theory of cochlear mechanics.
Fig.
4 The dot moves ellipsoidal and comes
outside the box. The diagonal gives the relation without electromotility. See
for animation of the movements: http://www.boystownhospital.org/Research/Areas/Neurobiological/MoreInfoComLab/cochlear_amp.asp
OHCs have evolved only in mammals. They improved the
hearing sensitivity compared to other classes of vertebrates which goes up to about
11 kHz (in some birds). However, their main function is to extend the hearing
range above 11 kHz, until about 200 kHz (maximum in some marine mammals). They
have also improved frequency selectivity of the TM-OHC-BM system. This allows
better frequency discrimination.
Adaptation to sound level
With
the Mossbauer technique measuring the Doppler shift in gamma radiation from a
small radioactive source placed directly on BM it was showed that the amplitude
of BM vibrations increased nonlinearly with increasing stimulus level. For
example, Fig. 5 shows the level dependence of the ratio of malleus vibration to
BM vibration. If the mechanics of the cochlea were linear, this ratio would be
independent of the stimulus level. However, the response ratio near fbest,
is largest when the signal level is smallest. This type of input/output
relationship is referred to as a compressive nonlinearity. When the animal
dies, or when OHCs are damaged, the magnitude of BM responses at low stimulus
levels becomes smaller near fbest, and its growth with stimulus
level becomes linear. The OHC
electromotility is the source of the compressive nonlinearity of BM: the weaker
the sound, the stronger the amplification of BM oscillations. This enables the
matching of the enormous range of sound pressure levels, some 107
compressed to a 104 range of variation of BM oscillations. Further
compression is provided by the steps in the processing sequence: BM oscillation
→IHC bundle deflection →receptor potential → action
potentials.
Fig. 5 Transfer
characteristic of BM displacement/malleus (= tympanic membrane) displacement.
Around fbest the ratio is strongly dependent on SPL, indicating the
non-linear character of the motion transduction from TM to BM. Symbols present
measurements and solid lines model fits. (From Mammano and Nobili).
Otoacoustic
emissions
Otoacoustic
emissions are based at the electromotil
activity of a restricted number of OHCs producing a too high cochlear
amplification. Low-level sounds of cochlear origin can be recorded from the
external auditory canal either spontaneously or evoked by sound stimuli.
Emissions can also be detected when electric current is applied to the cochlea.
It may possibly be caused by a reduced inhibitory efferent stimulation.
The mechanical feedback loop provided by the OHC must
be finely regulated to guarantee optimal functioning of the cochlear amplifier.
To cope with simultaneously occurring transient (sudden) and tonic (sustained)
stimuli the regulatory mechanisms should at least control the operating point
and gain of the OHC electromotility through a direct action of nerve efferents.
Efferent stimulation suppresses afferent sound-elicited activity of the
auditory nerve by the release of ACh on two time scales: a rapid action (tens
of milliseconds) is responsible for modulating nerve responses to transient
acoustic stimulation, whereas a slower action (tens of seconds) is thought to
protect the ear from acoustic overstimulation.
http://www.boystownhospital.org/Research/Areas/Neurobiological/MoreInfoComLab/cochmech.asp
(Research page Boys Town National Research Hospital)
Mammano F. and Nobili R., http://147.162.36.50/cochlea/index.htm
and http://147.162.36.50/cochlea/cochleapages/theory/index.htm
Nobili R, Mammano F and Ashmore JF. How well do we understand the
cochlea? Trends in Neurosciences
1998;21:159-167.