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Re: Answers, comments welcome.

Dear Randy, dear list,

   I really don't want to get into deep discussions about theories, but I feel 
that it is important (at least for list subscribers who have not spent some 
time inside the inner ear) to clarify what "the consensus of the field" is, at 
least from time to time.

The traveling wave "theory" is based on many OBSERVATIONS and MEASUREMENTS and 
provides a viable framework to explain lots of them. Yes, you can actually see 
a "traveling wave" in a cochlea, and you can measure responses in the inner 
ear with high precision with more advanced techniques (see BÃkÃsy, Khanna, 
Rhode, Patuzzi, Ruggero, Cooper, to name only a few). 

Where Willems states that "Without any doubt this is indicating that at least 
squaring of the input stimulus plays a dominating role" this was not observed 
in these measurements.

If you got the impression from Willems response that "slow" traveling waves 
with wavelengths much smaller than a meter violate all laws of physics, you 
can calm down. Just do an experiment with yelly to convince yourself from the 
opposite (and yes, the material properties of the inner ear structures are 
closer to yelly than steel, where wavelengths are actually in the dimensions 
Willems stated). And again, there is data, and you can actually see such 
microscopic waves, watch the Video from Freeman's lab:

My specific answer to Randy:
There is good news: to solve your question, you don't have to speculate, you 
can use data and experiments. Especially, I recommend you to install one of 
the models, which generate nerve-action potentials (e.g. from the Carney or  
Meddis groups). They are based on measurements (of course they will never be 
perfect, but for your question, they will do the trick). You can use them to 
simulate your idea with sufficient precision. If you have done that, you might 
conclude that your question can not be resolved by the cochlea alone, it 
highly depends on the processing of the grey material coming afterwards.

Best regards an nice holidays (at least for me)

Prof. Dr.-Ing. Werner Hemmert
Bio-Inspired Information Processing
IMETUM - Institute for Medical Engineering
Technische UniversitÃt MÃnchen
BoltzmannstraÃe 11
85748 Garching

Phone: +49 89 289 10853
Mobile: +49 162 2900427
Fax: +49 89 289 10805
e-mail: werner.hemmert@xxxxxx
Internet: http://www.bai.ei.tum.de

On Tuesday, August 14, 2012 12:09:14 AM Willem Christiaan Heerens wrote:
Dear Randy and List, Randy, in your message about dichotic stimulation of the 
basilar membrane [BM] you formulated your remarks and asked for answers and/or 
comments on the following topic: ** Do the BM's in a dichotic experiment using 
two harmonically related tones (e.g. 200/300 hz) have the same vibration 
profile or are they different? ** And you apologized in the following way: ** I 
don't know if this is beyond the scope of this forum in which case I 
apologize. However, if this topic is not too crazy, I would welcome any 
answers, guesses or speculations. ** To my opinion your remarks are to the 
highest level relevant for everybody who is involved in the research of our 
hearing sense, so also for members of this List. And in my view it is far from 
crazy. At the risk of fluttering the dovecote I want to give you my answers and 
comments you asked for. However for a better understanding of my comments I 
can only do this in two steps. Please let me first reopen as shortly as 
possible that other topic issue, because it is directly related with the setup 
of my present answer to you. In November/December last year we have had the 
discussion whether a traveling wave exists inside the cochlea or on the BM 
that transfers the sound pressure stimulus of a pure tone to the point where, 
for the corresponding frequency, the BM can resonate. Also the model that 
makes use of the transmission line concept was discussed then. I on my turn 
presented in that discussion session in a PDF the solution of the non-
stationary Bernoulli equation, that is perfectly well valid in the case of the 
push-pull movements of the perilymph inside the scala tympani [ST] and scala 
vestibuli [SV], while the in between embedded scala media [SM], filled with 
endolymph at rest, has substantial â and therefore not negligible â 
dimensions. According to hydrodynamic rules these dimensional conditions make 
that the hypothesis in which both the influence of the Reissner membrane and 
the content of the SM can be ignored and the cochlear duct can be considered 
as a folded tube with only the BM as an interface in between is definitely 
invalid. At the end of that discussion Dick Lion stated that in his opinion 
the local frequency dependent flexibility or compliance of the BM makes it 
possible that this membrane is bending outwards â a local movement of the BM 
towards the SV â and that this bending is the cause of evoking sound related 
stimuli in the BM, organ of Corti and finally via the auditory nerve to the 
auditory cortex. He therefore firmly disagreed with my point of view and my 
theoretical work couldnât convince him (and others on this List) that the 
functional mechanism in the cochlear partition might be completely different 
from what is assumed at the moment. Well like the well-known promoter of 
physics, MIT professor Walter Lewin, does in his magnificent physics courses, I 
have built my own demonstration equipment for clearly showing what happens on 
the walls of a duct in which an alternating flow in core direction is evoked. 
The one experimental set-up is extremely simple, but therefore also highly 
convincing. To mimic utmost compliance in the âwallsâ in one of the 
experiments I have hanged on thin wires in an open frame two sheets of paper 
that can move freely. Between the two I can evoke with a spatula an 
alternating flow parallel to the surfaces of the sheets of paper. And I have 
constructed a closed loop with a tube and a bellow, the latter centrally 
subdivided by a plate, with which I can create a push-pull flow in the tube, 
while in the other branch of the tube locally a flexible membrane is mounted in 
the wall, which registers what happens on the wall of the tube. The obtained 
results I found in both experiments? The evoked motion patterns are exactly 
identical to what I could predict out of the theory I have presented last year 
on this List. The two sheets of paper are not at all moving in outward 
direction as was suggested. They are moving in opposite direction, so towards 
the core line of the alternating flow. And under a steady alternating stimulus 
(with constant amplitude) they both do that with a stationary deflection on 
which an alternating deflection is superposed with doubled frequency. This 
indicates that both sheets experience the influence of an alternating and in 
average lower pressure evoked in the space between the two sheets. The tube 
experiment also shows that the membrane in the wall is always moving inwards â 
so towards the core line of the tube. And superposed on a constant deflection 
inwards the membrane also deflects periodically with double frequency related 
to the original stimulus frequency. Without any doubt this is indicating that 
at least squaring of the input stimulus plays a dominating role. [Note: To 
make it even more convincing for everyone I will place a video registration of 
these experiments fairly soon on internet, like Walter Lewin does with his 
physics courses.] For now the only clear and firm conclusion I can draw is that 
the suggestions on this item of Dick Lion and others are wrong. The medium in 
the tube is moving as a whole. And therefore these experimental results, in 
combination with the theoretical solution of the non-stationary Bernoulli 
equation, are one of the reasons that the transmission line concept cannot 
play a role in it either. The second reason for rejecting the traveling wave 
concept is the following: I also have studied the different possibilities for 
âtraveling wavesâ in literature. And then especially I have looked at the 
conditions, parameters and geometrical dimensions under which such waves can 
exist. In short (you donât need expensive literature retrievals, because you 
can read a summary of the possible wave forms in Wikipedia) we can state that 
there are three forms to distinguish: 1. Rayleigh waves Rayleigh waves are a 
type of surface acoustic waves which travel on solid materials. The typical 
speed of these waves is slightly less than that of so-called shear waves. And 
it is by a factor (dependent on the elastic constants) given by the bulk 
material. This speed is of the order of 2â5 km/s. For a sound signal with a 
1000 Hz frequency this means that the minimal wavelength is approximately 2 
meter. While the BM has a length of approximately 35 millimeter, it is 
impossible to make a realistic combination for application in the cochlea. 
Besides that Rayleigh waves are surface waves where the thickness of the 
material must be relatively high related to the concerned wavelength. With a 
fraction of a millimeter thickness for the BM you can forget that this type of 
wave can play a role in the BM vibrations. 2. Love waves In the field of 
elastodynamics, Love waves, named after A. E. H. Love, are described as 
horizontally polarized shear waves guided by an elastic layer, which is 
"welded" to an elastic half space (so a very thick part of bulk material) on 
one side while bordering a vacuum on the other side. In literature can be 
found that the wavelength of these waves is relatively longer than that of 
Rayleigh waves. And also these conditions and parameters are nowhere found in 
the cochlear partition. 3. Lamb waves Lamb waves propagate in solid plates. 
They are elastic waves whose particle motion lies in the plane that contains 
the direction of wave propagation and the plate normal (the direction 
perpendicular to the plate). In 1917, the English mathematician Horace Lamb 
published his classic analysis and description of acoustic waves of this type. 
The wave propagation velocities of the two possible modes in Lamb waves are 
comparable with that of the Rayleigh wave. And therefore they also donât 
provide for a possible application in the traveling wave description inside 
the cochlea. In other words: we also cannot make a realistic fit with Lamb 
waves inside the cochlea. Of course everybody can persist in believing that 
until now registered auditory experimental results justify the formulated 
hypothesis that such types of waves can exist in the cochlea. Then however you 
are forced to answer the following question: On what underlying physics 
grounds is it possible that material quantities and acoustic process 
parameters inside the cochlea can be altered in such a way that as a result 
the wavelength of 1.5 meter for a 1000 Hz stimulus in bulk perilymph fluid can 
be altered in less than 1.5 millimeter? As can be seen from the Rayleigh, Love 
and Lamb waves the circumstances and material properties cannot provide for a 
scaling factor better than 0.5 from bulk material sound velocity to the 
concerned type of wave. Be aware that inside the cochlea a scaling factor of 
0.001 or even smaller will have to be possible. This can be considered as 
completely impossible. What remains is that just as I stated before: The 
described non-stationary Bernoulli effect, that provides for the sound energy 
stimulus everywhere in front of the BM, is driving the BM vibrations. And dear 
Randy this last statement above is my answer to your following remark: ** I 
have always wondered about what drives BM vibrations ** It is the everywhere 
present sound energy stimulus that drives the BM. My following contribution 
will show the implication of all this for the rest of your request. Kind 
regards Willem Heerens