Re: A new paradigm?(On pitch and periodicity (was "correction to post")) (Willem Christiaan Heerens )


Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
From:    Willem Christiaan Heerens  <heerens1@xxxxxxxx>
Date:    Mon, 31 Oct 2011 16:57:58 -0400
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Peter van Hengel, Dick Lyon and other contributors, my apologies for the=20= late response to your contributions to this topic.=20 However in my opinion this subject is still far away from a satisfactory=20= result. And I prefer to give you a clear and well overthought reaction. Therefore let me first give you a comment on Peter=92s following reaction= to=20 Matt Flax: ** One small comment to your statement that there are only forward=20 traveling waves. I think much of the confusion stems from the fact that=20= the observed motion of the cochlear partition is often referred to as the= =20 traveling wave. In actual fact this is only a 'reflection' of the actual=20= wave which is traveling in the fluid. The fluid supports waves traveling=20= in both directions, but the unique properties of the cochlea cause only=20= the appearance of a forward traveling on the cochlear partition.** Yes indeed that is the explanation for the =91traveling wave hypothesis=92= =20 within the common paradigm. And if you want to explain a reported=20 apparently observed =91traveling wave=92 over the basilar membrane, runni= ng=20 from the base =96 near the round window =96 to the apex =96 near the=20 helicotrema, with a mathematical model designed by you, of course it is=20= legitimate to try this.=20=20 However in the background of all the exercises there remains to be=20 incorporated a constraint that cannot be ignored or disobeyed: the basics= =20 of such mathematical models must be in full agreement with the general=20= rules and laws of physics. I seriously hope that the AUDITORY List members agree with me that there=20= doesn=92t exist =96 beside general physics =96 a special cochlear physics= theory=20 with its own laws and rules, which are different from and occasionally=20= even at variance with the general ones. If not, we can end our discussion= =20 right away, because we then can only agree that we fundamentally disagree= . But let me comment on Peter=92s statement about the observed basilar=20 membrane traveling wave:=20 **In actual fact this is only a 'reflection' of the actual wave which is=20= traveling in the fluid.** I really must remind you to the fact that a mechanical vibration =96 and = the=20 sound stimulus is such a vibration =96 in a fluid, or in this case water=20= like perilymph, will always propagate with the speed of sound, which has=20= typically here the value of 1500 m/s. That is just one of those constraints dictated by general physics. And=20= with the equation that counts for the relation between sound velocity,=20= frequency and wavelength we simply can calculate that for a 1000 Hz=20 stimulus the corresponding wavelength in the perilymph is 1.5 meter. So=20= approximately equal to 50 times the length of the active partition of the= =20 basilar membrane.=20 That is the only reason why the round window is moving in opposite=20 direction related to the oval window. A widely reported always observed=20= phenomenon in experiments. And under the existing conditions in the cochlea there is no physics=20 ground for so-called =91slow waves=92 with wavelengths even in the order = of=20 fractions of a millimeter. With the same equation for the relation betwee= n=20 wave propagation velocity, frequency and wavelength as is used for=20 the =91fast=92 running waves here above. Just because such a slow wave demands the propagation of a row of=20 successively higher and lower pressure areas with sizes in the order of=20= those wavelengths and even smaller. And that is impossible in general=20 physics. The incompressibility of the perilymph fluid makes this=20 impossible. It cannot be that a mathematical wish for explaining the existence of a=20= hypothesized traveling wave with a small wavelength prescribes that=20 physics has to offer the possibility for such a slow wave. Just because=20= the general physics rule prescribes that wave propagation velocity equals= =20 frequency times wavelength. And therefore the only possibility that remains is that under the=20 incompressibility constraint the entire perilymph fluid column between=20= oval window =96 helicotrema =96 round window is moving as a whole, while = it is=20 stimulated by a mechanical vibration of the stirrup.=20=20=20 Peter you further stated: **The fluid supports waves traveling in both directions, but the unique=20= properties of the cochlea cause only the appearance of a forward travelin= g=20 on the cochlear partition.** If we look closer to the basilar membrane properties, we observe that=20 there exists a frequency-place related distributed resonance capability.=20= With a subdivision that has a logarithmical scale from apex to base. High= =20 resonance frequencies near the base and low resonance frequencies near th= e=20 apex. Actually this unique property is the cause that a stimulus, that is=20 equally present all over the length of the basilar membrane, evokes phase= =20 related movements which appear as a =91wave=92 that is always running fro= m=20 base to apex. And it is this =91wave=92 phenomenon that is erroneously interpreted as=20= the =91traveling wave=92 that transfers the sound stimulus.=20=20=20 And of course the perilymph fluid can be stimulated from both sides. Weve= r=20 and Lawrence have reported that already in 1950. They reported that=20 stimulating either the oval window or the round window results in=20 identical cochlear potentials.=20 But that doesn=92t imply that there have to run traveling waves in both=20= directions. We can only draw the conclusion that a perilymph push-pull caused by a=20= sound stimulus isn=92t dependent on the pathway that is chosen. Peter, you made the remark: ** If one wants to observe the reverse traveling waves in the cochlea it=20= is necessary to measure fluid velocity, which I believe is not yet=20 possible.** No indeed. A direct measurement of velocity inside the cochlea is known a= s=20 extremely difficult. So far every attempt fails, mostly because of the=20= intolerable disturbances of the properties in the location that has to be= =20 examined. This makes the experimental results unreliable. And non-invasiv= e=20 measurements still show not enough details of fluid movements. But from what really happens there we nevertheless can still make a=20 reliable imagination, which is simply based on physics and the=20 physiological properties and parameters which exist in the cochlea. Let us make an inventory of them. The physiological structure data: =95=09The walls of the cochlear envelope are extremely rigid. Hardly=20 compliant to not compliant at all. So bone conduction based on deformatio= n=20 of that envelope is not possible. =95=09The cochlea shaped cavity is subdivided into the perilymph filled=20= duct, which is folded at the apex and which parts are the scala vestibuli= =20 between oval window and apex and the scala tympani between apex and round= =20 window. =95=09In between these two scalae the third one =96 scala media =96 is=20= located, filled with endolymph. =95=09The partition between scala vestibuli and scala media is formed by=20= the Reissner membrane. This membrane is extremely thin, but on all=20 available electron microscope pictures it is observed as straight, except= =20 for M=E9ni=E8re cochlea, where it is curved into the direction of the sca= la=20 vestibuli. This membrane has compliance. =95=09The partition between the scala tympani and the scala media is=20 formed by the basilar membrane. This membrane has substantially more=20 volume, while both the inner and the outer hair cells are embedded in it= .=20 This membrane has a place located frequency dependent compliance. It can=20= be observed as a resonance device. =95=09The hair bundles of the outer hair cells are at their top=20 connected with the tectorial membrane, a rim structure that is completely= =20 located in the scala media and connected with the bony envelope of the=20= cochlea. =95=09At every location along the cochlear partition the cross sections=20= of scala tympani and scala vestibuli are practically equal in size. In=20= average the channel diameter is 0.3 mm. =95=09There exists a tapered shape in the perilymph duct, larger at the=20= base to smaller at the apex. =95=09The maximal deflections of the oval window and the round window=20 are estimated to be in the order of a few micrometers. =95=09Deflections of the basilar membrane also do not exceed a few=20 micrometers. Otherwise the hair bundles of the outer hair cells would be=20= damaged due to overstressing.=20=20=20 =20=20 The involved material quantities: =95=09The perilymph fluid in the scala vestibuli and scala tympani as=20 well as the endolymph fluid in the scala media has a density equal to tha= t=20 of water. So 1000 kg/m3. =95=09Both fluids are incompressible and have a low viscosity,=20 comparable with water. This can be considered in practice as =91viscous=20= free=92. =95=09The propagation velocity of acoustic vibrations in the perilymph=20= is 1500 m/s.=20 Cardinal fluid dynamics numbers: =95=09The main criterion for non-turbulent fluid flow in the cochlea is=20= the Reynolds number. Calculation in case of the highest hearable frequenc= y=20 stimulus of a 20 kHz vibration with an amplitude of 1 micrometer with a=20= dynamic viscosity coefficient equal to that of water: 0.001 Ns/m2 gives=20= for this Reynolds number a value of 36. For vibrations with lower=20 frequencies and with similar amplitudes this Reynolds number is=20 proportionally lower.=20 Hence the Reynolds number is for all situations far below the boundary of= =20 2000, the value that counts for upper boundary of the laminar flow=20 conditions. And therefore the perilymph flow inside the cochlea is=20 definitely non-turbulent.=20 All these aspects together result in the fact that it is allowed to=20 consider the perilymph movement inside the cochlea as a periodic movement= =20 that can be theoretically expressed by the non-stationary Bernoulli=20 equation. Just as I have done in the attached PDF in my message to the=20= AUDITORY List of Saturday, October 1, 2011. For those of you who think that I misuse the Navier-Stokes theory in the=20= case of the cochlear fluid dynamics I can point to the following=20 elucidating introductory explanation placed on-line on the Internet by th= e=20 Academic Medical Center of Amsterdam that I cite here: -- The Navier-Stokes equations are a set of equations that describe the=20= motion of fluids (liquids and gases, and even solids of geological sizes=20= and time-scales). These equations establish that changes in momentum=20 (acceleration) of the particles of a fluid are simply the product of=20 changes in pressure and dissipative viscous forces (friction) acting=20 inside the fluid. These viscous forces originate in molecular interaction= s=20 and dictate how sticky (viscous) a fluid is. Thus, the Navier-Stokes=20 equations are a dynamical statement of the balance of forces acting at an= y=20 given region of the fluid. They are one of the most useful sets of equations because they describe=20= the physics of a large number of phenomena of academic and economic=20 interest. They are useful to model weather, ocean currents (climate),=20 water flow in a pipe, motion of stars inside a galaxy, flow around a wing= =20 of an aircraft. They are also used in the design of aircraft and cars, th= e=20 study of blood flow, the design of power stations, the analysis of the=20= effects of pollution, etc. The Navier-Stokes equations are partial differential equations which=20 describe the motion of a fluid, so they focus on the rates of change or=20= fluxes of these quantities. In mathematical terms these rates correspond=20= to their derivatives. Thus, the Navier-Stokes for the simplest case of an= =20 ideal fluid (i.e. incompressible) with zero viscosity states that=20 acceleration (the rate of change of velocity) is proportional to the=20 derivative of internal pressure. Poiseuille=92s Law and Bernoulli=92s equ= ation=20 are special cases of 1D Navier-Stokes. The fluid motion is described in 3-D space, and densities and viscosities= =20 may be different for the 3 dimensions, may vary in space and time. Since=20= the flow can be laminar as well as turbulent, the mathematics to describe= =20 the system is highly complex.=20 In practice only the simplest cases can be solved and their exact solutio= n=20 is known. These cases often involve non turbulent flow in steady state=20= (flow does not change with time) in which the viscosity of the fluid is=20= large or its velocity is small (small Reynolds number).=20 For more complex situations, solution of the Navier-Stokes equations must= =20 be found with the help of numeric computer models, here called=20 computational fluid dynamics.=20 Even though turbulence is an everyday experience it is extremely hard to=20= find solutions for this class of problems. Often analytic solutions canno= t=20 be found. Reducing the models to 1D, as is often done in fluid dynamics of blood=20= vessels, makes the problem handsome. -- [See also: http://onderwijs1.amc.nl/medfysica/compendiumDT.htm edited by= =20 N. A. M. Schellart 2005] After studying my PDF that I sent to the List on October 1 2011, you can=20= see for yourself that I have derived the analytical solution for the non-= stationary non-viscous incompressible time dependent wiggle-waggle=20 movements directed along the core of the perilymph duct. Because in that=20= case the reduction of the complex set of Navier-Stokes equations to the=20= non-stationary Bernoulli equation is fully permitted. And this finally results in the fact that everywhere inside the perilymph= =20 duct the evoked pressure variations are proportional to the sound energy=20= stimulus. This means that by resonance in the basilar membrane, i.e. the frequency-= place related distributed resonance capability, the stimulus can evoke=20= simultaneously all the frequency contributions of the sound energy signal= ,=20 including the exact phase relation for each contribution, which will be=20= sent to the auditory cortex. Further details I will give in my answers to the comments of Dick Lyon=20= here below. Finally Peter you reacted to Matt Flax with: ** Model calculations clearly show the reverse traveling wave and produce= =20 results in accordance with data on OAEs (see e.g. the work of Mauermann e= t=20 al or Epp et al). ** Yes that is based on the =91transmission line model=92. And of course tha= t=20 will present a reverse traveling wave. The entire model that is used is=20= based on the hypothesis that there must exist and consequently must be=20= explained a traveling wave whatsoever.=20 However that is the cardinal subject of difference between your statement= s=20 and mine. In my concept, based on the Bernoulli solution, there still exists a =91w= avy=20 motion=92 on the basilar membrane, but that is the result of phase depend= ent=20 behavior.=20 Locations with higher resonance frequencies react in phase with the=20 frequency stimulus; at resonance locus this motion is 90 degrees behind i= n=20 phase; locations with lower resonance frequencies react 180 degrees=20 retarded in phase. And because higher resonance frequencies are found near the round window,= =20 while lower resonance frequencies are found near the helicotrema=20 the =91wave=92 always runs from base to apex. And as Tianying Ren et al.= also=20 experimentally detected: there doesn=92t exist a reversed traveling wave.= And now my reactions to the comments of Dick Lyon: Dick you remarked: ** Willem, your approach in which "the flow behaves as a parallel=20 streaming oriented along the core of the perilymph duct" and in=20 which "there exists only a contribution in the x-direction" is what might= =20 be called a "non-compliant membrane" approximation.** In strict theoretical terms you could name it as such, but in practice it= =20 means that the movements of the incompressible viscous-free perilymph, in= =20 the direction perpendicular to the core of the perilymph duct, are=20 negligibly small compared to the movement in the core direction. You commented also with: ** Generally, the BM is interpreted as being variably compliant (and the=20= RM very compliant), such that there is some velocity (and pressure=20 variation) ortogonal to the x dimension, which corresponds to BM=20 displacement. ** Regarding the first part of it, the compliance of the membranes, I agree=20= with you. And I have also used this frequency dependent =91compliance=92 = of=20 the basilar membrane in my description of the evoked movements in this=20= membrane due to a sinusoidal sound stimulus.=20 It results in a DC deflection all over the basilar membrane due to=20 the =91time average of the sound energy signal=92 and the locally evoked = AC or=20 frequency dependent deflection at the corresponding resonance locus with = a=20 doubled frequency. And it results in an all over the Reissner membrane=20= existing combination of a DC deflection towards the scala vestibuli and a= n=20 AC deflection with a doubled frequency. It isn=92t a basilar membrane movement due to an =91overpressure=92 cause= d by an=20 increase in pressure inside the perilymph. That is in essence the specifi= c=20 behavior of a potential flow =96 like this Bernoulli flow actually is =96= =20 where the decrease in internal pressure [delta p] is proportional to the=20= decrease in potential energy [E potential], while the kinetic energy [E=20= kinetic] of the entire perilymph mass [m] in the flow tube increases=20 proportionally to the fluid velocity [v] squared. Thereby potential energ= y=20 and kinetic energy in the potential flow remain always in balance. You commented: ** If you assume no BM displacement, then of course you have no traveling= =20 wave. ** Nowhere in my explanation have I stated that basilar membrane mobility=20= doesn=92t exist. Of course there exist basilar membrane displacements. But their influence= s=20 on the local cross section of the perilymph duct are rudimentary. And for clarity let us make an indicative calculation:=20 The average diameter of the perilymph duct is 0.3 mm. And let us assume=20= the cross section to be circular. Then the size of the surface can be=20 calculated as 0.0706 square mm. The local deflection of the basilar=20 membrane cannot be much larger than a few micrometers. Otherwise the hair= =20 bundles of the outer hair cells would be overstretched or even disrupted.= The width of the basilar membrane is approximately 0.1 mm. If that is=20 displaced 1 micrometer over its entire width, the corresponding surface o= f=20 that cross section is 0.0001 square mm.=20 This means that the cross section at the place of the membrane deflection= =20 is relatively 1.4 pro mille decreased. So you cannot maintain that this=20= will have a serious influence on the main fluid movements in the core=20 direction of the perilymph duct. You commented further: ** The BM (or the whole of scala media in your approximation) separates=20= the two parts of the folded duct in which you have a longitudinal pressur= e=20 gradient, so there will be a substantial pressure difference across it,=20= from the far-apart x locations (except near the apex where it folds). ** I am sorry that I have to tell you, but with this statement you show that= =20 you do not really understand the general mechanism of the potential flow.= =20=20 And I can explain this at best with the example of a straight tube in=20 which a (periodic) potential flow exists. For this flow condition the=20 fluid in the tube is incompressible and non-viscous and the flow isn=92t=20= turbulent, which means =91rotation free=92. Since there doesn=92t exist internal laminar friction [the fluid isn=92t=20= viscous] it will =91stream=92 along the core direction of the tube everyw= here=20 with the same velocity. In that case the (non-stationary) Bernoulli equation is valid and the=20 internal pressure in the tube is everywhere the same and given by the wel= l- known Bernoulli relation. The decrease in internal pressure in the fluid=20= is equal to half the density of the fluid multiplied with the square of=20= the fluid velocity. In case of the non-stationary Bernoulli flow, the=20 involved velocity in this equation is then a function of time. If we insert pressure sensors at two places along the tube in its wall,=20= each of the pressure sensors will detect a decrease in pressure=20 proportional to the square of the fluid velocity =96 in full accordance w= ith=20 the Bernoulli equation.=20 However, if we try to measure the pressure difference between the two=20 locations, we will find zero as the result. That is logic because the=20 fluid velocities in both cross sections are equal. However, if we want to measure the fluid velocity in the tube, we can use= =20 the solution found by Venturi. Then we have to place in the tube an=20 intersection in which the cross section along the length of that partitio= n=20 gradually and fluently decreases from the tube cross section to a minimum= =20 value and then fluently increases again to the size of the original tube=20= cross section. And let us place this Venturi tube in-between the two=20 original pressure sensors.=20 If we insert now in the wall of the narrowest cross section of that=20 Venturi tube a third pressure sensor, we will measure there an extra=20 decrease in pressure related to the other two pressure sensors.=20 The now measurable pressure difference between the Venturi pressure senso= r=20 and the pressure sensor either =91up-streams=92 or =91down-streams=92 is=20= proportional to the fluid velocity in the tube multiplied with the total=20= of the square of the ratio between tube cross section and Venturi cross=20= section minus 1. Hence there exists a lower pressure in the Venturi tube, but equal=20 pressures on both sides of the Venturi tube. And remark that in principle the Venturi tube in the potential flow isn=92= t=20 forming an obstacle in that flow. Otherwise there would exist a pressure=20= difference between locations on both sides of the Venturi tube.=20 Now we can make one further step: we can smoothly fold the tube in the=20= Venturi partition in such a way that the narrowest cross section also=20 forms the =91elbow=92 in the folded tube. [ let us name that the helicotr= ema]. Hence =96 contrary to what you suggested in your comment =96 under the=20= potential flow conditions inside the cochlea there doesn=92t exist a=20 longitudinal pressure gradient, which evokes a substantial pressure=20 difference across the helicotrema.=20 Finally we can place in-between the two parts of the tube [scala vestibul= i=20 and scala tympani] a third one [the scala media] that forms an=20 intersection of the two other ones.=20 As long as the cross sections of both perilymph ducts at some place x awa= y=20 from the base [oval and round window] are identical, the evoked pressures= =20 on both sides of the scala media will be directed outwards and equal.=20 Exactly as is shown in Fig. 3 on page 22 of our booklet =91Applying Physi= cs=20 Makes Auditory Sense=92. The movements shown in several animations on the Internet, where the=20 stapes activation creates =91waves=92 of higher frequency stimulus=20 contributions which leave the core flow in the scala vestibuli and let th= e=20 Reissner membrane and the basilar membrane simultaneously vibrate at a=20= location nearer to the base, while from that location in the scala tympan= i=20 a reverse =91wave=92 propagates toward the round window, is based on a=20= hypothesis for which I cannot find a sound physics principle.=20 [See for instance: http://www.blackwellpublishing.com/matthews/ear.html = ] Dick, you commented also: ** If you allow the pressure across the BM to deflect it, as we usually d= o=20 with membrane compliance, you get a very different analysis, based on the= =20 same physics but different mechanical approximations. In this analysis,=20= the v-squared pressure differences due to Bernoulli's law are generally=20= very small compared to the pressure differences accelerating the fluid=20= within the short wavelength of the traveling wave, so are neglected. ** Let me first calculate what pressure decrease will be evoked in front of=20= the basilar membrane by a stimulus of 1000 Hz which let the oval window=20= deflect with an amplitude of 2 micrometer. With the density of perilymph [ 1000 kg/m^3 ] the maximum pressure=20 decrease will be 72 mPa. Not really a low value. Another fact is that we also have to cope with the problem that the=20 pressure differences accelerating the fluid within the short wavelength o= f=20 the traveling wave =96 that would exist indeed in the =91transmission lin= e=92=20 hypothesis and in the companying mathematical model, which calculates=20 these hypothesized effects =96 have no physics ground to exist in the wig= gle- waggle movements of the perilymph. Finally you commented: ** Which approximation is better? Probably the one that yields a=20 traveling wave like the one seen in direct mechanical measurements, I=20 think.** Already years ago I corresponded with Tianying Ren, the man who did this=20= kind of mechanical measurements. On his request because those measurement= s=20 did not fit well within the ruling traveling wave paradigm. Actually they= =20 were flawed in that time by the auditory peers.=20 In 2008 De Boer et al. also reported that there were serious doubts about= =20 the hypothesized existence of reversed traveling waves. Only=20 forward =91waves=92 on the basilar membrane could be observed. He also=20= suggested that in the first place there must be found an explanation that= =20 can dispose this newly arisen anomaly.=20 The observed =91wave phenomena=92 on the basilar membrane resemble the fo= rms=20 that are shown in the following animations, which can be downloaded from=20= the Internet: =09http://lab.rockefeller.edu/hudspeth/graphicalSimulations or: =09http://www.youtube.com/watch?v=3DdyenMluFaUw These simulated animations also resemble very well with the phase wave=20= phenomena which I have calculated and which I have presented in brief in=20= our booklet for one sinusoidal stimulus.=20 The traveling wave you refer to in your comment here above is by far not=20= an accomplished fact. Therefore I hope you will agree with me that the best theoretical=20 description of the functioning of our hearing sense is the one that is in= =20 the first place in agreement with physics, describes and explains the=20 experimental findings very well even in detail, can cope with the existin= g=20 anomalies, and can predict correctly in detail new and until now unknown=20= hearing and auditory perception phenomena. And I am convinced that under these requirements our hearing paradigm is = a=20 very serious candidate.=20 Kind regards, Pim Heerens


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