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Re: mechanical cochlear model
Just for the record, I did not side with the travelling wave hypothesis.
I did want to say that there appears to be a divergence on what
'travelling wave' means. It would be good if someone knowledgeable
gave an authoritative definition. If possible make it operational
by saying how we can recognize that there is one, and how we would
rule out the opposite hypothesis.
In the physics courses I took way back when, travelling waves were
introduced in the context of propagation on a string or in a
waveguide. Since the cochlea differs considerably from a uniform
string or waveguide it's not immediately obvious what a travelling
wave is in this context. The physics are quite different. In
particular the fact that propagation is quasi-instantaneous in the
liquid surrounding the membrane makes the system very different from
a string (or the surface of the sea).
The 'simple-account-for-students-in-cognitive-sciences' didn't
mention a travelling wave.
Best,
Alain
I agree with Reinhart Frosch and Alain de Cheveigne and Dave
Mountain on this. The cochlear traveling wave may have some open
issues, but to say that "its function in hearing is not yet
universally appreciated" is misleading, and I think a bit
disingenuous.
It's OK to investigate the open issues, and to use them to motivate
new ideas that depart from the generally accepted view. But I think
it's not a good idea to misrepresent the extent to which the ideas
are accepted by the mainstream hearing community. In the case of
the traveling wave, the acceptance is pretty much universal, and has
been for quite a long time; the agreement of theory and experiment
gets better over time, as experimental data get better and as
analysis techniques get more mature and models converge on physical
measurements.
With respect to Jont Allen's 2001 remark that "the discrepancy in
frequency selectivity between basilar membrane and neural responses
has always been, and still is, the most serious problem for the
cochlear modelling community" (in his chapter "Nonlinear Cochlear
Siganl Processing" in Jahn and Santos-Sacchi "Physiology of the
Ear"), I had encountered that myself recently, and was wondering
what's behind it. Jont goes on to say, in italics even, "In my
view, this discrepancy is one of the most basic unsolved problems of
cochlear modeling." and then "Progress on this front has been
seriously confounded by the uncertainty in, and the interpretation
of, the experimental data."
It's a great chapter, and I agree with Jont on many of his points
and attitudes, but I still wonder what he was poking at with that
paragraph. My view is a little different: active hydromechanical
models are able to yield transfer functions and tuning curves and
nonlinearities that are pretty much like what we see in both
mechanical and neural data (FTCs, Weiner kernels, 2TS curves, etc.).
The problem may be in his intepretation of "frequency selectivity",
as he sometimes turns FTCs upside-down and compares them with
transfer functions, as in his Figure 19-12 that he refers back to
later as an example of a neural/mechanical mismatch. That seems
like an odd mistake to make in a chapter on nonlinearity, but it is
one that is widespread in the hearing literature, not unique to
Jont, and one that has a history of introducing confusion about
sharpness in different ways of looking at a system.
Jont also says, a few pages earlier, "In fact, according to
measurements made over the last 20 years, the response of the
basilar membrane to a pure tone can change in amplitude by more than
5 orders of magnitude per millimeter of distance along the basilar
membrane (ie, 300 dB/octave is equivalent to 100 dB/mm in the cat
cochlea)." This strikes me as another misapplication of linear
thinking to a nonlinear system. If the FTC requires an increase of
5 orders of magnitude to get a given response when the frequency is
increased by 1/3 octave, which I can accept as roughly credible,
then that has to be understood as a combination of a fairly sharp
high-frequency rolloff and a fairly strong nonlinear level
dependence. If the response compression slope is about 1/3 above
CF, then the compression explains about 2/3 of the steepness of the
300 dB/octave slope, so the estimated change in response with place
for a given pure tone needs to be cut by a factor of three, to about
1.7 orders of magnitude, not 5. This is the kind of discrepancy
that I'd think would be included when saying "Progress on this front
has been seriously confounded by the uncertainty in, and the
interpretation of, the experimental data," but perhaps Jont is
thinking of some other problems.
The open problems that Jont points out, of getting good models of
two-tone suppression and upward spread of masking, that unify
mechanical and neural data, are indeed important points where
modelers have more work to do. I think the situation is actually in
not such bad shape, though. I don't see any real basis for thinking
that a new paradigm is what's needed at this time to make progress,
and I don't think that's what Jont is saying, either, unless he's
telling us to stop assuming that the system has active amplification.
Jont, can you fill us in? Has the problem been updated in your
opinion since 2001? Are you referring to interpretations of active
amplification as part of the problem?
Dick