Subject: Re: mechanical cochlear model From: Peter van Hengel <pwj.vanhengel@xxxxxxxx> Date: Mon, 15 Mar 2010 13:07:28 +0100 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--0016e6d56640979beb0481d5b9e5 Content-Type: text/plain; charset=ISO-8859-1 Dear Michael and others, thanks very much for your response to my mail. I will try to respond to some of your comments and questions, although I have to admit that some of the details of the questions are not quite clear to me. Perhaps I have been out of the research community for too long, or it is because I prefer to keep things simple because I am a bit simple. Referring to the hair cells acting as pressure sensors: I was under the impression that the entire cochlea was filled with fluid, some of it in hair cells and other cells. If there are air bubbles in hair cells or other types of (compressible) media somewhere inside the cochlea I stand corrected. Wit respect to prestin or other substances being able to deform and so sense pressure: if there is a possibility to deform these substances than it would work. My point is that if something (anything) in the cochlea is deforming, then there has to be fluid motion (even if the motion is caused by a compression wave). If there is fluid motion and there is a flexible boundary with a restoring force then there will be a (traveling) wave on this boundary, according to everything I know about fluid mechanics. There are lots of elements in the cochlea which have mass and a restoring force (stiffness), which means they will act as resonators. So, as I said in my mail, it is not a question of traveling wave OR resonators, it is a combination of both. The fact that there is a traveling wave implies that the resonators are not independent, as they are modeled in e.g. a filterbank. There is a continuity in the motion of the basilar membrane caused by the continuity of the fluid surrounding it. This does not mean that filterbank models are useless, they have proven to be very useful. But they contain a simplification which people using them should simply be aware of. With respect to the transfer of energy you mention, this is a bit tricky and there are some good papers on this which you might read, but I'll try an explanation anyway. The large speed of sound in water means that effectively every motion anywhere in the cochlea is 'felt' by all locations on the BM almost instantaneously. (In a WKB or Green's function approach I think the compressibility is neglected which implies that it is instantaneous in these models.) So all locations will react to an external (or internal) stimulus at once. But each section of the BM will also immediately feel the other locations start to react. One might say that all section together 'agree' on a pattern of motion which looks like a travelling wave. The pattern of motion is governed by the mechanics of the BM and by the fluid. The fluid properties combined with the restoring force in the membrane dictate that the pattern will look like a traveling wave. Like you, I stick to the passive case for safety reasons. But even in the active case, if there is fluid motion and a flexible boundary with a restoring force there will be a traveling wave. I hope this has answered some of your questions. Kind regards, Peter 2010/3/12 Michael RAPSON <MICHAEL.RAPSON@xxxxxxxx> > Dear Peter and the list, > > Thank you for your discussion of the basic fluid mechanics, I want to > comment and ask a follow up question on this aspect of it, but first let me > comment on your concluding remarks re compression waves. My understanding is > that people advocating the compression wave as the stimulus accept the need > for compressible elements in the outer hair cell and have put forward > arguments for their existence (see Bell (2008) for one example I have > recently read). > > As you say the traveling wave comes out of the basic fluid dynamics > equations and passive basilar membrane boundary conditions. The WKB > approximation generally provides better insight into the form of the > solution than numerical techniques such as integration of Greens functions > and predicts a traveling wave in the passive cochlea. However, on one point > at least I think that looking at the Greens function can give more insight: > it allows us to discuss the effect of motion at one point on the basilar > membrane on the pressure (force) at another. Nobili and Mammano (1993) FIG. > A3 is a convenient figure to discuss this from. It clearly shows that the > motion of a single point on the basilar membrane causes a similar pressure > over a wide range of locations, but points in the near vicinity with an > exaggerate pressure (due to the 'singular part'). > > If there were a fluid that did not have the singular part of the Greens > function and the pressure exerted was constant spatially then each radial > segment of the basilar membrane / organ of Corti complex would absorb or > radiate real and reactive power to distant segments as easily as nearby. > This suggests that the segments could be rearranged arbitrarily without > affecting the behavior of the individual segments or the collection. In this > thought experiment any traveling wave that exists seems to be merely a > coincidence of the power requirements of each individual segment at a given > instance. > > However the slight spatial roll off of the Greens function combined with > the effect of the singular part causes displacements of nearby segments to > have a larger effect on each other than on distant segments. This ensures > more effective power transfer between nearby segments and seems to be > essential to a traveling wave that carries energy. Each segment still only > acts by absorbing or radiating real and reactive power from each other via > the fluid, but now there is a preference for power in the vicinity. > > As to my question, surely the initial response of the basilar membrane to a > pure tone is an important thing to consider on this topic? I realize that > getting reliable data for a steady state pure tone is already challenging, > but I think the cochlear response to the onset of a band limited signal > would be very interesting. The prevalent view of the behavior of the > traveling wave seems to be that during the first few cycles this band > limited signal would propagate from the stapes towards the best place > carrying energy. A plausible alternative is that energy radiated by the > stapes would be stored and re-emitted by the ENTIRE basilar membrane, in > differing proportions. The radial segments would start in phase with each > other since each experiences a force at the same instant, but would quickly > fall into their known phase relationship due to the fluid coupling. In this > scenario energy transfer is though of as closer to a point to point > transmission than a transfer with the traveling wave. (Although as discussed > above there seems to be a preference to energy transfer in the vicinity). > > I would like to hear your view on whether the alternative description of > the energy transfer is compatible with the physics of the passive cochlea. > If it is it seems to be at least compatible with the resonance theory. It > would suggest that care should be taken in the importance placed on > unwrapped phase plots as evidence of the traveling wave in frequency domain > models and the WKB approximation, although I know that phase delay has > support from other sources. I also acknowledge that the rapid fall off after > the best place lends more support to the prevailing traveling wave view than > the alternative interpretation, although this result might also come out in > the maths for the alternative view. The time domain signal required to test > this should be free of higher order harmonics, since these will stimulate > the basilar membrane basal of the best place and thus are hard to generate. > > In summary my current view is that the traveling wave observed in the > physics of the passive cochlea is in part simply a feature of the > arrangement of the radial segments, given that to some extent all the > segments are coupled and can transfer energy point to point. A second > important part is that local energy transfer is slightly assisted by the > increased local coupling. Would you agree with this position or do you see a > fundamental error in it? Studying the onset of pure tones seems to a good > way to evaluate the relative importance of these effects. > > I have deliberately only discussed the passive case to avoid extending the > previous debate about the active mechanisms at work, although I know that > they are the major focus of current work. I would however appreciate it if > we could continue discussing this passive case, since it is adequate for > understanding the question I pose. Hopefully if we come to an agreement on > the passive case we can extend the discussion to the active elements. > > All your thoughts are much appreciated and apologies for length, > > Michael > > > > > > Bell (2008) Andrew Bell, "The pipe and the pinwheel: Is pressure an > effective stimulus for the 9 + 0 primary cilium?", Cell Biology > International 32 (2008) 462-468 > Nobili and Mammano (1993): R. Nobili and F. Mamano, "Biophysics of the > cochlea: Linear approximation", J. Acoust. Soc. Am. Vol. 93, No. 6, June > 1993 > > > >>> On 2010/03/12 at 04:07 PM, in message > <20100312142543.815B989AA@xxxxxxxx>, Peter van Hengel > <pwj.vanhengel@xxxxxxxx> wrote: > > Dear list, > > > > With a background in fluid mechanics perhaps my perspective on the > traveling > > wave helps the discussion. > > > > I don't think there is a question whether or not there is a traveling > wave > > in the cochlea. Fluid mechanics dictates that there has to be one. > > > > The confusion comes - I think - from comparing the basilar memebrane with > a > > string where the energy is passed on through the string and it is that > same > > string which is showing the movement. In this respect the comparison with > > surface waves on water is much appropriate. The fluid-air interface is > > showing the movement, but it is the underlying fluid which passes > > on the motion. Imagine a pond surface covered with ducks. Imagine it to > be > > covered so densely you cannot see the water surface. When the water is > set > > in motion (not neccessarily at its > > surface), the ducks will move. This motion will look like a wave and I > guess > > everyone would agree with the use of the term travelling wave in this > case. > > The energy causing the > > ducks to move is not passed on from one duck to the other, but stems from > > the motion of > > the fluid. > > > > Likewise in the cochlea the BM motion is caused by motion of the fluid. > The > > fact that we > > have fluid on both sides of the BM, whereas in the example we have fluid > > below and air on > > top can be shown (mathematically) to be of no consequence for the > principle. > > Also the > > fact that in the example the restoring force acting on the ducks is > gravity, > > whereas in > > the cochlea it is the BM stiffness does not affect this story. > > > > The main problem with the resonator/resonance theory (at least in the > > versions I know) is > > that the motion of neighbouring resonators is independent. In the example > > neighouring ducks can not move independently because their motion is > linked > > through the motion of the underlying (continous) water. > > > > Complicating factor in the discussion is perhaps that in the cochlea, the > > restoring force being stiffness combined inevitably with mass, we > > automatically get resonators. So in my view it > > is not a question of resonance OR travelling wave. It has to be a bit of > > both. > > > > Fluid mechanics dictates that there is a travelling wave on the basilar > > membrane unless cochlear fluid is unlike any other fluid I know. The > > question that may remain is whether this wave motion is what causes the > > effective stimulation of haircells. But there should not be a question > > whether or not there is a traveling wave, even if it has not been shown > > definitively in measurements. > > > > The problem I see with a compression wave being the stimulus and the > > haircells acting as pressure sensors is that. This assumes that the > > haircells will be compressed by a pressure acting on them form the > outside. > > However, the haircells are filled with fluid themselves and there will be > no > > pressure difference between the inside and outside of the cell. This > implies > > that the cell wil not deform and I do not quite see how the sensor would > > then operate. (But the fact that I don't see it does not mean it > impossible, > > of course...). > > > > The references to texts already given by dr Frosch and others are > excellent > > and I don't have much else to add. > > > > All the best, > > Peter van Hengel > > > > > ______________________________________________________________________________________________ > > UNIVERSITY OF CAPE TOWN > > This e-mail is subject to the UCT ICT policies and e-mail disclaimer > published on our website at > http://www.uct.ac.za/about/policies/emaildisclaimer/ or obtainable from > +27 21 650 4500. This e-mail is intended only for the person(s) to whom it > is addressed. If the e-mail has reached you in error, please notify the > author. If you are not the intended recipient of the e-mail you may not use, > disclose, copy, redirect or print the content. If this e-mail is not related > to the business of UCT it is sent by the sender in the sender's individual > capacity. > > > _____________________________________________________________________________________________________ > > --0016e6d56640979beb0481d5b9e5 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <div>Dear Michael and others,</div> <div>=A0</div> <div>thanks very much for your response to my mail. I will try to respond t= o some of your comments and questions, although I have to admit that some o= f the details of the questions are not quite clear to me. Perhaps I have be= en out of the research community for too long, or it is because I prefer to= keep things simple because I am a bit simple.</div> <div>=A0</div> <div>Referring to the hair cells acting as pressure sensors: I was under th= e impression that the entire cochlea was filled with fluid, some of it in h= air cells and other cells. If there are air bubbles in hair cells or other = types of (compressible) media somewhere inside the cochlea I stand correcte= d.</div> <div>Wit respect to prestin or other substances being able to deform and so= sense pressure: if there is a possibility to deform these substances than = it would work. My point is that if something (anything) in the cochlea is d= eforming, then there has to be fluid motion (even if the motion is caused b= y a compression wave). If there is fluid motion and there is a flexible bou= ndary with a restoring force then there will be a (traveling) wave on this = boundary, according to everything I know about fluid mechanics.</div> <div>=A0</div> <div>There are lots of elements in the cochlea which have mass and a restor= ing force (stiffness), which means they will act as resonators. So, as I sa= id in my mail, it is not a question of traveling wave OR resonators, it is = a combination of both. </div> <div>The fact that there is a traveling wave implies that the resonators ar= e not independent, as they are modeled in e.g. a filterbank. There is a con= tinuity in the motion of the basilar membrane caused by the continuity of t= he fluid surrounding it. This does not mean that filterbank models are usel= ess, they have proven to be very useful. But they contain a simplification = which people using them should simply be aware of.</div> <div>=A0</div> <div>=A0With respect to the transfer of energy you mention, this is a bit t= ricky and there are some good papers on this which you might read, but I= 9;ll try an explanation anyway. The large speed of sound in water means tha= t effectively every motion anywhere in the cochlea is 'felt' by all= locations on the BM almost instantaneously. (In a WKB or Green's funct= ion approach I think the compressibility is neglected which implies that it= is instantaneous in these models.) So all locations will react to an exter= nal (or internal) stimulus at once. But each section of the BM will also im= mediately feel the other locations start to react. One might say that all s= ection together 'agree' on a pattern of motion which looks like a t= ravelling wave. The pattern of motion is governed by the mechanics of the B= M and by the fluid. The fluid properties combined with the restoring force = in the membrane dictate that the pattern will look like a traveling wave.<b= r> </div> <div>Like you, I=A0stick to the passive case for safety reasons. But even i= n the active case, if there is fluid motion and a flexible boundary with a = restoring force there will be a traveling wave.</div> <div>=A0</div> <div>I hope this has answered some of your questions.</div> <div>Kind regards,</div> <div>Peter <br></div> <div class=3D"gmail_quote">2010/3/12 Michael RAPSON <span dir=3D"ltr"><<= a href=3D"mailto:MICHAEL.RAPSON@xxxxxxxx">MICHAEL.RAPSON@xxxxxxxx</a>>= </span><br> <blockquote style=3D"BORDER-LEFT: #ccc 1px solid; MARGIN: 0px 0px 0px 0.8ex= ; PADDING-LEFT: 1ex" class=3D"gmail_quote">Dear Peter and the list,<br><br>= Thank you for your discussion of the basic fluid mechanics, I want to comme= nt and ask a follow up question on this aspect of it, but first let me comm= ent on your concluding remarks re compression waves. My understanding is th= at people advocating the compression wave as the stimulus accept the need f= or compressible elements in the outer hair cell and have put forward argume= nts for their existence (see Bell (2008) for one example I have recently re= ad).<br> <br>As you say the traveling wave comes out of the basic fluid dynamics equ= ations and passive basilar membrane boundary conditions. The WKB approximat= ion generally provides better insight into the form of the solution than nu= merical techniques such as integration of Greens functions and predicts a t= raveling wave in the passive cochlea. However, on one point at least I thin= k that looking at the Greens function can give more insight: it allows us t= o discuss the effect of motion at one point on the basilar membrane on the = pressure (force) at another. Nobili and Mammano (1993) FIG. A3 =A0is a conv= enient figure to discuss this from. It clearly shows that the motion of a s= ingle point on the basilar membrane causes a similar pressure over a wide r= ange of locations, but points in the near vicinity with an exaggerate press= ure (due to the 'singular part').<br> <br>If there were a fluid that did not have the singular part of the Greens= function and the pressure exerted was constant spatially then each radial = segment of the basilar membrane / organ of Corti complex would absorb or ra= diate real and reactive power to distant segments as easily as nearby. This= suggests that the segments could be rearranged arbitrarily without affecti= ng the behavior of the individual segments or the collection. In this thoug= ht experiment any traveling wave that exists seems to be merely a coinciden= ce of the power requirements of each individual segment at a given instance= .<br> <br>However the slight spatial roll off of the Greens function combined wit= h the effect of the singular part causes displacements of nearby segments t= o have a larger effect on each other than on distant segments. This ensures= more effective power transfer between nearby segments and seems to be esse= ntial to a traveling wave that carries energy. Each segment still only acts= by absorbing or radiating real and reactive power from each other via the = fluid, but now there is a preference for power in the vicinity.<br> <br>As to my question, surely the initial response of the basilar membrane = to a pure tone is an important thing to consider on this topic? I realize t= hat getting reliable data for a steady state pure tone is already challengi= ng, but I think the cochlear response to the onset of a band limited signal= would be very interesting. The prevalent view of the behavior of the trave= ling wave seems to be that during the first few cycles this band limited si= gnal would propagate from the stapes towards the best place carrying energy= . A plausible alternative is that energy radiated by the stapes would be st= ored and re-emitted by the ENTIRE basilar membrane, in differing proportion= s. The radial segments would start in phase with each other since each expe= riences a force at the same instant, but would quickly fall into their know= n phase relationship due to the fluid coupling. In this scenario energy tra= nsfer is though of as closer to a point to point transmission than a transf= er with the traveling wave. (Although as discussed above there seems to be = a preference to energy transfer in the vicinity).<br> <br>I would like to hear your view on whether the alternative description o= f the energy transfer is compatible with the physics of the passive cochlea= . If it is it seems to be at least compatible with the resonance theory. It= would suggest that care should be taken in the importance placed on unwrap= ped phase plots as evidence of the traveling wave in frequency domain model= s and the WKB approximation, although I know that phase delay has support f= rom other sources. I also acknowledge that the rapid fall off after the bes= t place lends more support to the prevailing traveling wave view than the a= lternative interpretation, although this result might also come out in the = maths for the alternative view. The time domain signal required to test thi= s should be free of higher order harmonics, since these will stimulate the = basilar membrane basal of the best place and thus are hard to generate.<br> <br>In summary my current view is that the traveling wave observed in the p= hysics of the passive cochlea is in part simply a feature of the arrangemen= t of the radial segments, given that to some extent all the segments are co= upled and can transfer energy point to point. A second important part is th= at local energy transfer is slightly assisted by the increased local coupli= ng. Would you agree with this position or do you see a fundamental error in= it? Studying the onset of pure tones seems to a good way to evaluate the r= elative importance of these effects.<br> <br>I have deliberately only discussed the passive case to avoid extending = the previous debate about the active mechanisms at work, although I know th= at they are the major focus of current work. I would however appreciate it = if we could continue discussing this passive case, since it is adequate for= understanding the question I pose. Hopefully if we come to an agreement on= the passive case we can extend the discussion to the active elements.<br> <br>All your thoughts are much appreciated and apologies for length,<br><br= >Michael<br><br><br><br><br><br>Bell (2008) Andrew Bell, "The pipe and= the pinwheel: Is pressure an effective stimulus for the 9 + 0 primary cili= um?", Cell Biology International 32 (2008) 462-468<br> Nobili and Mammano (1993): R. Nobili and F. Mamano, "Biophysics of the= cochlea: Linear approximation", J. Acoust. Soc. Am. Vol. 93, No. 6, J= une 1993<br><br><br>>>> On 2010/03/12 at 04:07 PM, in message<br> <<a href=3D"mailto:20100312142543.815B989AA@xxxxxxxx">201= 00312142543.815B989AA@xxxxxxxx</a>>, Peter van Hengel<br> <div> <div></div> <div class=3D"h5"><<a href=3D"mailto:pwj.vanhengel@xxxxxxxx">pwj.vanhen= gel@xxxxxxxx</a>> wrote:<br>> Dear list,<br>><br>> With a back= ground in fluid mechanics perhaps my perspective on the traveling<br>> w= ave helps the discussion.<br> ><br>> I don't think there is a question whether or not there is = a traveling wave<br>> in the cochlea. Fluid mechanics dictates that ther= e has to be one.<br>><br>> The confusion comes - I think - from compa= ring the basilar memebrane with a<br> > string where the energy is passed on through the string and it is that= same<br>> string which is showing the movement. In this respect the com= parison with<br>> surface waves on water is much appropriate. The fluid-= air interface is<br> > showing the movement, but it is the underlying fluid which passes<br>&= gt; on the motion. Imagine a pond surface covered with ducks. Imagine it to= be<br>> covered so densely you cannot see the water surface. When the w= ater is set<br> > in motion (not neccessarily at its<br>> surface), the ducks will mo= ve. This motion will look like a wave and I guess<br>> everyone would ag= ree with the use of the term travelling wave in this case.<br>> The ener= gy causing the<br> > ducks to move is not passed on from one duck to the other, but stems f= rom<br>> the motion of<br>> the fluid.<br>><br>> Likewise in th= e cochlea the BM motion is caused by motion of the fluid. The<br>> fact = that we<br> > have fluid on both sides of the BM, whereas in the example we have flu= id<br>> below and air on<br>> top can be shown (mathematically) to be= of no consequence for the principle.<br>> Also the<br>> fact that in= the example the restoring force acting on the ducks is gravity,<br> > whereas in<br>> the cochlea it is the BM stiffness does not affect = this story.<br>><br>> The main problem with the resonator/resonance t= heory (at least in the<br>> versions I know) is<br>> that the motion = of neighbouring resonators is independent. In the example<br> > neighouring ducks can not move independently because their motion is l= inked<br>> through the motion of the underlying (continous) water.<br>&g= t;<br>> Complicating factor in the discussion is perhaps that in the coc= hlea, the<br> > restoring force being stiffness combined inevitably with mass, we<br>&= gt; automatically get resonators. So in my view it<br>> is not a questio= n of resonance OR travelling wave. It has to be a bit of<br>> both.<br> ><br>> Fluid mechanics dictates that there is a travelling wave on th= e basilar<br>> membrane unless cochlear fluid is unlike any other fluid = I know. The<br>> question that may remain is whether this wave motion is= what causes the<br> > effective stimulation of haircells. But there should not be a question= <br>> whether or not there is a traveling wave, even if it has not been = shown<br>> definitively in measurements.<br>><br>> The problem I s= ee with a compression wave being the stimulus and the<br> > haircells acting as pressure sensors is that. This assumes that the<br= >> haircells will be compressed by a pressure acting on them form the ou= tside.<br>> However, the haircells are filled with fluid themselves and = there will be no<br> > pressure difference between the inside and outside of the cell. This i= mplies<br>> that the cell wil not deform and I do not quite see how the = sensor would<br>> then operate. (But the fact that I don't see it do= es not mean it impossible,<br> > of course...).<br>><br>> The references to texts already given b= y dr Frosch and others are excellent<br>> and I don't have much else= to add.<br>><br>> All the best,<br>> Peter van Hengel<br><br> <br><br></div></div>_______________________________________________________= _______________________________________<br><br>UNIVERSITY OF CAPE TOWN<br><= br>This e-mail is subject to the UCT ICT policies and e-mail disclaimer pub= lished on our website at <a href=3D"http://www.uct.ac.za/about/policies/ema= ildisclaimer/" target=3D"_blank">http://www.uct.ac.za/about/policies/emaild= isclaimer/</a> or obtainable from +27 21 650 4500. This e-mail is intended = only for the person(s) to whom it is addressed. If the e-mail has reached y= ou in error, please notify the author. If you are not the intended recipien= t of the e-mail you may not use, disclose, copy, redirect or print the cont= ent. If this e-mail is not related to the business of UCT it is sent by the= sender in the sender's individual capacity.<br> <br>_______________________________________________________________________= ______________________________<br><br></blockquote></div><br> --0016e6d56640979beb0481d5b9e5--