# Re: Cochlea Amplifier models : a new list

`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`