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Re: Cochlear travelling wave. An epiphenomenon?
Dear Antony and List:
I have no problem accepting your idea that when a compressional wave meets
an impedance discontinuity then acoustic forces are created across it which
lead to movement of the partition. Indeed, this is one of the principal
features of my resonance theory, where, at SPLs above about 60 dB,
appreciable acoustic forces are generated across the tectorial membrane
(which generate ripples at the vestibular lip which slowly propagate to the
I think you would agree, Antony, that in the case under discussion (a
short-circuit at the basal end), that the acoustic forces would act across
the tectorial membrane, not the basilar membrane? The TM, as a gel, has
distinctive mechanical properties such that the speed of sound in it is
quite different to what it is in the cochlear fluids, leading to the
impedance discontinuity we speak of.
You would not assert, I suppose, that in this case the pressure is generated
across the BM, which is basically comprised of water?
The difficulty I see for the TW theory is that it holds that the TW is
generated by volume flow considerations (not speed of sound ones): that is,
TW theory holds that differential pressure is generated across the partition
because the helicotrema is so tiny that it has appreciable impedance to
fluid flow at frequencies above about 100 Hz (in other words, its proponents
want the helicotrema to be just be a pressure-relief pathway for DC
pressures). If we accept this arrangement, then, from conservation of mass
arguments, when (at acoustic frequencies) the stapes pushes in and out, the
BM has to give way and move down and up at its weakest point - where its
mass and compliance present minimum impedance at that frequency.
But if you abandon the volume flow considerations (and in particular the
idea that differential pressure does all the work in sustaining the TW),
then there is no real difference between the TW theory and the resonance
theory. In other words, as we have discussed here recently, the TW will then
be an epiphenomenon. The one remaining distinctive feature of the TW picture
(which Jont Allen pointed out) has then been lost - that is, the coupling
between the partition elements due to oscillating fluid elements. This
coupling feature - which is a supposition, remember, not an experimental
observation - is not a part of the resonance theory. The oscillating fluid
elements cannot be sustained whenever there is an acoustic short-circuit
between the scalae, whether it comes about by the helicotrema having
acoustic impedance larger than TW proponents believe (as I assert) or by
having yet another gaping hole at the basal end. These fluid elements
disappear because the fluid just slips through the hole(s), canceling the
pressure difference, rather than bouncing up and down on either side of the
BM as they are forced to do if the scalae are effectively separate. This is
why I raised the issue: you cannot have a full-blown TW _and_ a hole in the
partition offering zero hydraulic resistance.
I think we might both agree that a more detailed investigation of the
hydromechanics/acoustics of the cochlea and its partition is needed. Both
the TW theory and the resonance theory would benefit from experimental
acoustic measurements. What is the actual acoustic impedance of the
helicotrema? What is the actual acoustic impedance of the TM? What is the
acoustic impedance of the BM? We do not know.
We do know that many sorts of wave-propagation modes can be established in
layered media [see refs below], but which mode dominates in the intact
cochlea is unknown. Cochleas with holes drilled in them can only be
misleading from an acoustical point of view. Until we know more, I am
proposing that the generation of forces across an acoustically opaque
tectorial membrane, initiating slow ripples from the vestibular lip, is a
likely scenario consistent with all observations. The resonance theory I put
forward is able to account for the observation and experiment outlined in
your post below; in particular, a 4-5 cycle delay occurs simply because, as
you will see from a cross-sectional diagram of the partition, there are 4 or
5 wavelengths of ripple on the TM between the vestibular lip and the IHC
(with 1 wavelength counted as the distance between OHC1 and 3).
You may prefer a TW theory because it has more advanced mathematical
formalism, but from an observational position it has difficulties, as I
mentioned before. It cannot account for why the cross-sectional area of the
helicotrema can be 1/4th that of the scalae yet still have relatively high
acoustical impedance, why additional holes in the partition do not affect
hearing (even in humans), why the Q of the ear is so high, why the BM can be
ossified without compromising hearing, and how mere electron-volts of
acoustic energy can be efficiently funneled to the cilia (without requiring
the whole partition to go through an intricate wholescale up and down
movement). I would also be grateful if someone could clearly explain how TW
theory accounts for spontaneous otoacoustic emissions.
In the end, we will choose the theory that best explains current
observations, not the one with the largest pre-existing body of mathematics.
Of course, we need more than assertions and counter-assertions. Ultimately,
we need data.
Brekhovskikh, L.M. (1980) Waves in Layered Media (Academic Press: N.Y.)
Tolstoy, I. (1973) Wave Propagation (McGraw-Hill: N.Y.)
From: AUDITORY Research in Auditory Perception
[mailto:AUDITORY@LISTS.MCGILL.CA]On Behalf Of Antony Locke
Sent: Saturday, 8 July 2000 12:56
Subject: Re: Cochlear travelling wave. An epiphenomenon?
Dear Neil, Andrew and List
Neil and Andrew refer to a comparative approach in our discussions on the
validity of the travelling wave model. I agree that in general the study
across species is, and has been, fruitful. Unfortunately, my limited
knowledge doesn't span peripheral auditory systems across species; to
clarify I was considering cochlear mechanics as applied to humans+rodents;
apologies for any confusion. However, just because the travelling wave (TW)
is postulated, say, for the human cochlea doesn't necessarily say anything
about the mechanisms involved in other species; the configurations and
therefore the mechanisms involved may differ considerably.
Andrew pointed out:
1. "the crocodile ear and that of many birds incorporates a 'cochlear
2. Tonndorf's post-mortem findings of large impedance discontinuities in
cochleae of normal hearing humans.
...and was interested to hear a TW explanation.
A couple of points are worth noting:-
Firstly, the role of the fast compressional (common-mode) wave in
initiating a TW. Consider the case where the stimulus is not applied to
the stapes, but at the apex. Von Bekesy did this and observed a TW
initiated at the conventional place (i.e. at the base) which propagated
towards the source. This finding can be explained as a result of a fast
wave launched at the stimulus site, which travels towards the base, and due
to the impedance mismatch at the boundary, i.e. oval and round windows,
leads to an apical TW. The argument also holds for bone conduction. The
important point is the existence of a mismatch in the impedance presented
to the fast wave propagating through the scala vestibuli to that presented
to the fast wave in the scala typani; this leads to a pressure gradient
across the cochlear partition. The effective site for launching the TW may
not be at the base, but just apical to the impedance discontinuity.
Secondly, the possibility of evanescent modes. If evanescent modes exist
then tunnelling could arise.
This, though, is in the realm of speculation.
My original point posted to the list was concerned with the most basic
description of energy flow in the cochlea:-
Observation: a highly graded anisotropic cochlear partition (Voldrich,
Experiment: asymmetrically tuned cochlear partition responses with large
phase lags (approx. 4 - 5 cycles) (Rhode, 1971).
Analysis: dispersive hydromechanical waves - cochlear travelling waves
When compared to experiment, there are quantitative limitations to the TW
model in some regions of parameter space. The limitations lead to
questions such as, how to include nonlinearity, what about 2 or 3 degrees
of freedom, the role of the tectorial membrane, is an active mechanism
necassary etc. People have integrated additional elements to the TW model
with varying degrees of success in order to address these questions. In
essence, the discussion over the past 2 weeks comes down to: are we willing
to disregard, or build upon, the TW model because of these limitations?