Re: Cochlear travelling wave. An epiphenomenon? (Andrew Bell )

Subject: Re: Cochlear travelling wave. An epiphenomenon?
From:    Andrew Bell  <bellring(at)SMARTCHAT.NET.AU>
Date:    Sun, 9 Jul 2000 12:47:58 +1000

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 IHC). 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. Andrew Bell _____________________________________ Brekhovskikh, L.M. (1980) Waves in Layered Media (Academic Press: N.Y.) Tolstoy, I. (1973) Wave Propagation (McGraw-Hill: N.Y.) _____________________________________ -----Original Message----- From: AUDITORY Research in Auditory Perception [mailto:AUDITORY(at)LISTS.MCGILL.CA]On Behalf Of Antony Locke Sent: Saturday, 8 July 2000 12:56 To: AUDITORY(at)LISTS.MCGILL.CA 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 shunt'", and 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, 1978). Experiment: asymmetrically tuned cochlear partition responses with large phase lags (approx. 4 - 5 cycles) (Rhode, 1971). Analysis: dispersive hydromechanical waves - cochlear travelling waves (Lighthill, 1991). 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? Kind regards Antony Locke

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