Re: Answers, comments welcome. (Willem Christiaan Heerens )

Subject: Re: Answers, comments welcome.
From:    Willem Christiaan Heerens  <heerens1@xxxxxxxx>
Date:    Mon, 13 Aug 2012 18:09:14 -0400

Dear Randy and List, Randy, in your message about dichotic stimulation of the basilar membrane= =20 [BM] you formulated your remarks and asked for answers and/or comments on= =20 the following topic: ** Do the BM's in a dichotic experiment using two harmonically related to= nes=20 (e.g. 200/300 hz) have the same vibration profile or are they different? = ** And you apologized in the following way: =20 ** I don't know if this is beyond the scope of this forum in which case I= =20 apologize. However, if this topic is not too crazy, I would welcome any=20= answers, guesses or speculations. ** To my opinion your remarks are to the highest level relevant for everybod= y=20 who is involved in the research of our hearing sense, so also for members= of=20 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=20= comments you asked for. However for a better understanding of my comments I can only do this in t= wo=20 steps. Please let me first reopen as shortly as possible that other topic issue,= =20 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=20 traveling wave exists inside the cochlea or on the BM that transfers the=20= sound pressure stimulus of a pure tone to the point where, for the=20 corresponding frequency, the BM can resonate. Also the model that makes u= se=20 of the transmission line concept was discussed then. I on my turn presented in that discussion session in a PDF the solution o= f=20 the non-stationary Bernoulli equation, that is perfectly well valid in th= e=20 case of the push-pull movements of the perilymph inside the scala tympani= =20 [ST] and scala vestibuli [SV], while the in between embedded scala media=20= [SM], filled with endolymph at rest, has substantial =96 and therefore no= t=20 negligible =96 dimensions. According to hydrodynamic rules these dimensional conditions make that th= e=20 hypothesis in which both the influence of the Reissner membrane and the=20= content of the SM can be ignored and the cochlear duct can be considered = as=20 a folded tube with only the BM as an interface in between is definitely=20= invalid. At the end of that discussion Dick Lion stated that in his opinion the lo= cal=20 frequency dependent flexibility or compliance of the BM makes it possible= =20 that this membrane is bending outwards =96 a local movement of the BM tow= ards=20 the SV =96 and that this bending is the cause of evoking sound related st= imuli=20 in the BM, organ of Corti and finally via the auditory nerve to the audit= ory=20 cortex.=20 He therefore firmly disagreed with my point of view and my theoretical wo= rk=20 couldn=92t convince him (and others on this List) that the functional=20 mechanism in the cochlear partition might be completely different from wh= at=20 is assumed at the moment. Well like the well-known promoter of physics, MIT professor Walter Lewin,= =20 does in his magnificent physics courses, I have built my own demonstratio= n=20 equipment for clearly showing what happens on the walls of a duct in whic= h=20 an alternating flow in core direction is evoked. The one experimental set-up is extremely simple, but therefore also highl= y=20 convincing. To mimic utmost compliance in the =91walls=92 in one of the experiments I= have=20 hanged on thin wires in an open frame two sheets of paper that can move=20= freely. Between the two I can evoke with a spatula an alternating flow=20= parallel to the surfaces of the sheets of paper. And I have constructed a closed loop with a tube and a bellow, the latter= =20 centrally subdivided by a plate, with which I can create a push-pull flow= in=20 the tube, while in the other branch of the tube locally a flexible membra= ne=20 is mounted in the wall, which registers what happens on the wall of the=20= tube.=20 The obtained results I found in both experiments?=20=20 The evoked motion patterns are exactly identical to what I could predict = out=20 of the theory I have presented last year on this List.=20 The two sheets of paper are not at all moving in outward direction as was= =20 suggested. They are moving in opposite direction, so towards the core lin= e=20 of the alternating flow. And under a steady alternating stimulus (with=20= constant amplitude) they both do that with a stationary deflection on whi= ch=20 an alternating deflection is superposed with doubled frequency. This indicates that both sheets experience the influence of an alternatin= g=20 and in average lower pressure evoked in the space between the two sheets.= =20=20=20=20 The tube experiment also shows that the membrane in the wall is always=20= moving inwards =96 so towards the core line of the tube. And superposed o= n a=20 constant deflection inwards the membrane also deflects periodically with=20= double frequency related to the original stimulus frequency. Without any doubt this is indicating that at least squaring of the input=20= stimulus plays a dominating role. [Note: To make it even more convincing for everyone I will place a video=20= registration of these experiments fairly soon on internet, like Walter Le= win=20 does with his physics courses.]=20 For now the only clear and firm conclusion I can draw is that the=20 suggestions on this item of Dick Lion and others are wrong. The medium in= =20 the tube is moving as a whole. And therefore these experimental results, = in=20 combination with the theoretical solution of the non-stationary Bernoulli= =20 equation, are one of the reasons that the transmission line concept canno= t=20 play a role in it either.=20 The second reason for rejecting the traveling wave concept is the followi= ng: I also have studied the different possibilities for =91traveling waves=92= in=20 literature. And then especially I have looked at the conditions, paramete= rs=20 and geometrical dimensions under which such waves can exist. In short (you don=92t need expensive literature retrievals, because you c= an=20 read a summary of the possible wave forms in Wikipedia) we can state that= =20 there are three forms to distinguish: 1.=09Rayleigh waves=20 Rayleigh waves are a type of surface acoustic waves which travel on solid= =20 materials.=20 The typical speed of these waves is slightly less than that of so-called=20= shear waves. And it is by a factor (dependent on the elastic constants)=20= given by the bulk material. This speed is of the order of 2=965 km/s. For a sound signal with a 1000 Hz frequency this means that the minimal=20= wavelength is approximately 2 meter. While the BM has a length of=20 approximately 35 millimeter, it is impossible to make a realistic=20 combination for application in the cochlea. Besides that Rayleigh waves are surface waves where the thickness of the=20= material must be relatively high related to the concerned wavelength.=20 With a fraction of a millimeter thickness for the BM you can forget that=20= this type of wave can play a role in the BM vibrations. 2.=09Love waves In the field of elastodynamics, Love waves, named after A. E. H. Love, ar= e=20 described as horizontally polarized shear waves guided by an elastic laye= r,=20 which is "welded" to an elastic half space (so a very thick part of bulk=20= material) on one side while bordering a vacuum on the other side. In=20 literature can be found that the wavelength of these waves is relatively=20= longer than that of Rayleigh waves. And also these conditions and parameters are nowhere found in the cochlea= r=20 partition.=20 3.=09Lamb waves Lamb waves propagate in solid plates. They are elastic waves whose partic= le=20 motion lies in the plane that contains the direction of wave propagation = and=20 the plate normal (the direction perpendicular to the plate). In 1917, the= =20 English mathematician Horace Lamb published his classic analysis and=20 description of acoustic waves of this type. The wave propagation velocities of the two possible modes in Lamb waves a= re=20 comparable with that of the Rayleigh wave. And therefore they also don=92= t=20 provide for a possible application in the traveling wave description insi= de=20 the cochlea.=20 In other words: we also cannot make a realistic fit with Lamb waves insid= e=20 the cochlea. Of course everybody can persist in believing that until now registered=20= auditory experimental results justify the formulated hypothesis that such= =20 types of waves can exist in the cochlea. Then however you are forced to=20= answer the following question: On what underlying physics grounds is it possible that material quantitie= s=20 and acoustic process parameters inside the cochlea can be altered in such= a=20 way that as a result the wavelength of 1.5 meter for a 1000 Hz stimulus i= n=20 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 a= nd=20 material properties cannot provide for a scaling factor better than 0.5 f= rom=20 bulk material sound velocity to the concerned type of wave. Be aware that inside the cochlea a scaling factor of 0.001 or even smalle= r=20 will have to be possible. This can be considered as completely impossible= .=20=20 What remains is that just as I stated before: The described non-stationary Bernoulli effect, that provides for the soun= d=20 energy stimulus everywhere in front of the BM, is driving the BM vibratio= ns.=20 And dear Randy this last statement above is my answer to your following=20= 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 r= est=20 of your request. Kind regards Willem Heerens

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