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Re: Cochlea Amplifier models : a new list
Dear A. J.
I agree with most of your characterisation of the current travelling wave (TW) theory. However, one aspect that is disputed by several theoreticians is the assertion that it is the impedance gradient that determines the direction of propagation of the TW. In the TW theory as given by, say, de Boer (1996), the TW can propagate in either direction along the BM. If a source is located at a point along the BM, it can (in this theory) propagate as a TW in both directions along the BM, provided it couples to TW motion. This is the explanation given for both distortion product and reflection otoacoustic emissions. Similarly a hypothetical BM with no impedance gradient at all would still allow a TW propagate from base to apex along the BM. So on this theory the TW is a true wave, the BM velocity obeying a version of the wave equation.
Contrary to the above, some authors state that it is the BM impedance gradient that determines the direction of TW propagation (e.g., Pickles, Intro to Physiology of Hearing). This belief may have arisen from an experiment by Wever & Lawrence (1954) which seemed to show that a source located at the apex caused a TW to be launched from the base to apex. However, Lighthill (1981, p. 178) argues that this was because the Wever & Lawrence apical source coupled to the fast (compressive) wave, which then progated to the base where it encountered the asymetrical impedances of the oval and round windows, which thus launched the TW, which is excited by the asymmetric "push-pull" of the two windows. So it was not the BM gradient that caused this effect, but the nature of the source (it coupled to the fast wave), and the impedance asymmetry.
Thus, according to Lighthill, de Boer, and others (eg. Shera, I think), the BM impedance gradient does not determine the TW direction: the TW can propagate away from a source like any other wave. (There is a complication that the TW cannot propagate along the BM in the mass-controlled region, but that's a separate issue.)
de Boer, E. (1996) ?Mechanics of the Cochlea: Modeling Efforts? in P. Dallos, A. N. Popper, R. R. Fay (Ed.), The Cochlea, Springer-Verlag, New York, pp. 258-317.
Lighthill, M. J. (1981) ?Energy flow in the cochlea? Journal of Fluid Mechanics, 106, pp. 149-213.
Shera CA, Tubis A, Talmadge CL, de Boer E, Fahe PF, Guinan JJ Jr.(2007) Allen-Fahey and related experiments support the predominance of cochlear
slow-wave otoacoustic emissions.' J Acoust Soc Am. 2007 Mar;121(3):1564-75.
Shera CA, Tubis A, Talmadge CL.'Do forward- and backward-traveling waves occur within the cochlea? Countering the critique of Nobili et al.' J Assoc Res Otolaryngol. 2004 Dec;5(4):349-59.
>>> "A.J. Aranyosi" <aja@xxxxxxx> 09/10/2007 17:51 >>>
Dear Matt and list,
Thank you for this summary - I think it provides a good framework for
discussing the relative merits of various models, and the problems that
these models are trying to solve. I'd like to start by summarizing the
traveling wave concept, since some of the people reading this list are
new to the field and could benefit from such a (most likely overly)
simplified primer. After that I'll point out some of the problems I see
with the simplest formulation of this idea, and how various cochlear
models try to address these problems.
When the stapes pushes in at the oval window, it causes an equal volume
displacement at the round window. This volume displacement can reach
the round window either through the helicotrema (which is generally
believed to be a significant pathway only for the lowest frequencies) or
through the basilar membrane (BM). When one section of the BM is
deflected, it displaces a certain amount of fluid. Because the cochlear
fluids are incompressible and the walls are rigid, this displaced fluid
must propagate longitudinally. This propagated fluid in turn applies
pressure to the BM at a different longitudinal position. This pressure
causes the BM at that location to deflect, which in turn leads to more
longitudinal fluid propagation, and this whole process repeats at a new
location. A gradient in the impedance of the BM imposes a preferred
direction on this propagation, so that BM displacement appears to travel
in a wave from base to apex; however, the energy itself is carried
longitudinally by the fluid rather than by the BM. In other words, the
traveling wave is a direct consequence of the incompressibility of the
cochlea and its contents. It's worth noting here that Andrew Bell has
proposed that the incompressibility constraint may not hold, and that
OHCs may be direct pressure sensors.
In many ways the traveling-wave model is overy simplistic. The first is
that the entire cochlear partition is simplified into a flat ribbon that
can be described by a point impedance. However, the organ of Corti has
a complex, evolutionarily conserved structure that suggests that it may
exhibit multiple modes of motion, so the point impedance approach may
not fully capture the dynamics of cochlear motion. One simple example
of this problem is that the BM moves transversely, but hair bundles are
sensitive to radial deflections, so at the very least there must be a
mode converter between the two.
Second, the classical traveling-wave model ignores longitudinal coupling
of the tissues in the cochlea. Such coupling could potentially
propagate a significant amount of energy longitudinally, so there could
be multiple pathways for energy storage and propagation in the cochlea.
de Boer has argued that any "non-classical" cochlear model (i.e., one
that includes longitudinal coupling among tissues) can be re-cast as a
classical model, but this process can remove the physiological
significance of the model parameters.
Third, we know that OHCs amplify the motion of the BM. However, they
also form part of the moving structure, and so cannot exert a net force
on this structure in the simple traveling-wave formulation. One
possible solution to this problem is the "sandwich" model concept
proposed by de Boer and by Hubbard and Mountain, in which OHCs excite a
difference-mode motion between the BM and the reticular lamina. These
models directly incorporate the idea that there are multiple modes of
motion within the cochlea.
Fourth, as Martin has pointed out earlier, there is a large disconnect
between the threshold of sensitivity (i.e., how small of a displacement
can cause IHCs to release neurotransmitter) and the threshold of
amplification (i.e., how small of a displacement can be amplified by
OHCs). That is, passive deflections of the BM at the threshold of
hearing are not large enough to gate transduction channels in OHCs,
which is presumably a necessary step in cochlear amplification. At
least two alternate solutions to this problem have been proposed. The
first is that displacements at the OHC bundles are much larger (by about
a factor of 1000) than displacements at the BM. The second is that OHCs
use stochastic resonance to provide noisy amplification of otherwise
undetectable signals, and the mechanical filtering of the cochlea
removes most of the noise.
One thing that is common among most current cochlear models is that they
all assign a great deal of significance to the motion of structures
within the organ of Corti. Unfortunately, our current best measurements
of cochlear function in vivo primarily show BM motion only, so we can
only distinguish between these models based on functional
interpretations of indirect measurements. Fortunately new techniques
such as OCT will allow measurements of the motion of structures internal
to the organ of Corti, so we can start resolving some of these issues
experimentally. In my mind there is such a close correlation between
measurements of BM motion and of auditory nerve fiber responses that
it's hard to believe that BM motion is not involved in cochlear
function. However, with the list I presented above it's also hard to
believe that BM motion is the entire story.
Matt Flax wrote:
> After our discussion last week, I have made a new list of possible
> physiological Cochlea Amplifiers (some of these are weakly
> physiologically based). I currently count six.
> Can anyone think of other physiologically based CAs to add to the
> list ?
> In no particular order :
> a] Oscillators : Van Der Pol type oscillators, which I believe
> began with Johannesma  b] Squirting wave : Andrew Bell's Organ of
> Corti squirting amplifier  c] Dual resonance : Martin Braun's dual
> resonance model  d] Feedback amp. : Zwicker's feedback amplifier
>  e] Hopf amplifier : Hopf bifurcation augmenting the travelling
> wave [5,6] f] Active TW : Active travelling wave amplifiers - of
> which I believe there are many, I reference only one 
> thanks Matt