Re: Cochlea Amplifier models : a new list

[Ben Lineton <bl@xxxxxxxxxxxxxxxx>]

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.


Ben Lineton

>>> "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.

-A.J.

Matt Flax wrote:
>  Hello,
>
>  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 [1] b] Squirting wave : Andrew Bell's Organ of
>  Corti squirting amplifier [2] c] Dual resonance : Martin Braun's dual
>  resonance model [3] d] Feedback amp.  : Zwicker's feedback amplifier
>  [4] 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 [7]
>
>  thanks Matt
>