Subject: Re: Laws of physics and old history; BM stiffness. From: David Mountain <dcm@xxxxxxxx> Date: Mon, 14 Nov 2011 09:20:59 -0500 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--0015174488a2749c6304b1b2941d Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable There are two modern sets of BM stiffness data, one from our lab, the other from the Northwestern group. Naidu, R.C. and Mountain, D.C. (1998). Measurements of the stiffness map challenge a basic tenet of cochlear theories. Hear. Res. 124: 124-131. [PDF]<http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/publi= cations/journal/NaiduMountain1998.pdf> Emadi G, Richter CP, Dallos P. (2004) Stiffness of the gerbil basilar membrane: radial and longitudinal variations. J Neurophysiol. 2004 Jan;91(1):474-88 The problem with treating the basilar membrane as a beam is that there can be significant longitudinal coupling along the basilar membrane: Naidu, R.C. and Mountain, D.C. (2001). Longitudinal coupling in the basilar membrane. J. Assoc. Res. Otolaryngol. 3:257-67. [PDF]<http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/publi= cations/journal/NaiduMountain2001.pdf> Also, both the tension and the amount of collagen in the basilar membrane changes with longitudinal location. Naidu, R.C. and Mountain, D.C. (2007) Basilar membrane tension calculations for the gerbil cochlea. J. Acoust. Soc. Am. 121:994-1002 [PDF]<http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/publi= cations/journal/NaiduMountain2007.pdf> In the case of the gerbil, the BM dimensions vary in a manner contrary to the conventional wisdom. With the exception of the hook region, the width of the basilar membrane changes little from base to apex and actually increases in thickness from base to apex. On the other hand, in cetaceans, the width and thickness vary significantly from base to apex much as one would expect if the material properties were uniform and the beam equation applies. On Fri, Nov 11, 2011 at 6:35 AM, reinifrosch@xxxxxxxx < reinifrosch@xxxxxxxx> wrote: > Hello! > > The following is a reaction to an earlier post of this thread: > > As already posted some years ago, it appears possible to me that the > stiffness S [Newtons per m^3] of the mammalian cochlear basilar membrane > (BM) decreases by several orders of magnitude from base to apex. If the > elements of the BM are treated as elastic beams, then the following formu= la > for S is obtained: > > S =3D n * Y * (delta-z)^3 / w^4, > > where delta-z is the beam thickness, w is the beam length (equal to the B= M > width), and Y is Young's modulus of the beam material (elasticity modulus= , > Newtons per m^2); the integer n depends on the way in which the beams are > fixed, at their ends, to the walls of the cochlear channel. If the beams > are clamped, then n =3D 60, if not, then n =3D 10. > > Fig. 11-73 of von Bekesy's book "Experiments in Hearing" (1960) yields a > human BM stiffness decrease of only two orders of magnitude from base to > apex. Has that experiment been re-done? > > > Reinhart Frosch, > Dr. phil. nat., > CH-5200 Brugg. > reinifrosch@xxxxxxxx . > > ----Urspr=FCngliche Nachricht---- > Von: rsran@xxxxxxxx > Datum: 09.11.2011 20:17 > An: <AUDITORY@xxxxxxxx> > Betreff: Re: Laws of physics and old history (A new paradigm?(On pitch an= d > periodicity (was "correction to post"))) > > --=20 David C. Mountain, Ph.D. Professor of Biomedical Engineering Boston University 44 Cummington St. Boston, MA 02215 Email: dcm@xxxxxxxx Website: http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/ Phone: (617) 353-4343 FAX: (617) 353-6766 Office: ERB 413 --0015174488a2749c6304b1b2941d Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable There are two modern sets of BM stiffness data, one from our lab, the other= from the Northwestern group.<div><br></div><div><span class=3D"Apple-style= -span" style=3D"color: rgb(34, 34, 34); font-family: arial, verdana, helvet= ica, sans-serif; font-size: 12px; line-height: 18px; background-color: rgb(= 242, 242, 242); ">Naidu, R.C. and Mountain, D.C. (1998).=A0 Measurements of= the stiffness map challenge a basic tenet of cochlear theories.=A0 Hear. R= es. 124: 124-131.=A0</span><a href=3D"http://www.bu.edu/hrc/research/labora= tories/auditory-biophysics/publications/journal/NaiduMountain1998.pdf" styl= e=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0= px; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left= : 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width:= 1px !important; border-left-width: 0px; border-style: initial; border-colo= r: initial; outline-width: 0px; outline-style: initial; outline-color: init= ial; font-size: 12px; font-family: arial, verdana, helvetica, sans-serif; v= ertical-align: baseline; color: rgb(80, 147, 177); border-bottom-style: dot= ted !important; border-bottom-color: rgb(204, 204, 204) !important; text-de= coration: none; line-height: 18px; text-align: left; background-color: rgb(= 242, 242, 242); ">[PDF]</a></div> <div>Emadi G<span class=3D"Apple-style-span" style=3D"font-family: arial, h= elvetica, sans-serif; font-size: 12px; line-height: 18px; background-color:= rgb(255, 255, 255); ">,=A0</span><span class=3D"highlight" style=3D"color:= rgb(51, 51, 51); border-bottom-width: 0px; border-bottom-style: initial; b= order-bottom-color: initial; font-family: arial, helvetica, sans-serif; fon= t-size: 12px; line-height: 18px; background-color: rgb(255, 255, 255); ">Ri= chter</span><font class=3D"Apple-style-span" color=3D"#333333" face=3D"aria= l, helvetica, sans-serif"><span class=3D"Apple-style-span" style=3D"border-= bottom-style: initial; border-bottom-color: initial; font-size: 12px; line-= height: 18px; background-color: rgb(255, 255, 255);">=A0</span></font>CP<sp= an class=3D"Apple-style-span" style=3D"font-family: arial, helvetica, sans-= serif; font-size: 12px; line-height: 18px; background-color: rgb(255, 255, = 255); ">,=A0</span><font class=3D"Apple-style-span" color=3D"#333333" face= =3D"arial, helvetica, sans-serif"><span class=3D"Apple-style-span" style=3D= "border-bottom-style: initial; border-bottom-color: initial; font-size: 12p= x; line-height: 18px; background-color: rgb(255, 255, 255);">Dallos P</span= ></font><span class=3D"Apple-style-span" style=3D"font-family: arial, helve= tica, sans-serif; font-size: 12px; line-height: 18px; background-color: rgb= (255, 255, 255); ">. =A0(2004)=A0</span><span class=3D"highlight" style=3D"= font-family: arial, helvetica, sans-serif; line-height: 18px; background-co= lor: rgb(255, 255, 255); ">Stiffness</span><span class=3D"Apple-style-span"= style=3D"font-family: arial, helvetica, sans-serif; line-height: 18px; bac= kground-color: rgb(255, 255, 255); ">=A0</span><span class=3D"Apple-style-s= pan" style=3D"font-family: arial, helvetica, sans-serif; line-height: 18px;= background-color: rgb(255, 255, 255); ">of the gerbil</span><span class=3D= "Apple-style-span" style=3D"font-family: arial, helvetica, sans-serif; line= -height: 18px; background-color: rgb(255, 255, 255); ">=A0</span><span clas= s=3D"highlight" style=3D"font-family: arial, helvetica, sans-serif; line-he= ight: 18px; background-color: rgb(255, 255, 255); ">basilar membrane</span>= <span class=3D"Apple-style-span" style=3D"font-family: arial, helvetica, sa= ns-serif; line-height: 18px; background-color: rgb(255, 255, 255); ">: radi= al and longitudinal variations.=A0</span>J Neurophysiol.<span class=3D"Appl= e-style-span" style=3D"font-family: arial, helvetica, sans-serif; line-heig= ht: 15px; background-color: rgb(255, 255, 255); ">=A02004 Jan;91(1):474-88<= /span></div> <div><span class=3D"Apple-style-span" style=3D"font-family: arial, helvetic= a, sans-serif; background-color: rgb(255, 255, 255); "><span class=3D"Apple= -style-span" style=3D"line-height: 15px;"><br></span></span></div><div><spa= n class=3D"Apple-style-span" style=3D"font-family: arial, helvetica, sans-s= erif; background-color: rgb(255, 255, 255); "><span class=3D"Apple-style-sp= an" style=3D"line-height: 15px;">The problem with treating the basilar memb= rane as a beam is that there can be significant longitudinal coupling along= the basilar membrane:</span></span></div> <div><span class=3D"Apple-style-span" style=3D"font-family: arial, helvetic= a, sans-serif; background-color: rgb(255, 255, 255); "><span class=3D"Apple= -style-span" style=3D"line-height: 15px;"><br></span></span></div><div><spa= n class=3D"Apple-style-span" style=3D"color: rgb(34, 34, 34); font-family: = arial, verdana, helvetica, sans-serif; font-size: 12px; line-height: 18px; = background-color: rgb(242, 242, 242); ">Naidu, R.C. and Mountain, D.C. (200= 1). Longitudinal coupling in the basilar membrane. J. Assoc. Res. Otolaryng= ol.=A0 3:257-67.=A0</span><a href=3D"http://www.bu.edu/hrc/research/laborat= ories/auditory-biophysics/publications/journal/NaiduMountain2001.pdf" style= =3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0p= x; padding-top: 0px; padding-right: 0px; padding-bottom: 0px; padding-left:= 0px; border-top-width: 0px; border-right-width: 0px; border-bottom-width: = 1px !important; border-left-width: 0px; border-style: initial; border-color= : initial; outline-width: 0px; outline-style: initial; outline-color: initi= al; font-size: 12px; font-family: arial, verdana, helvetica, sans-serif; ve= rtical-align: baseline; color: rgb(80, 147, 177); border-bottom-style: dott= ed !important; border-bottom-color: rgb(204, 204, 204) !important; text-dec= oration: none; line-height: 18px; text-align: left; background-color: rgb(2= 42, 242, 242); ">[PDF]</a></div> <div><span class=3D"Apple-style-span" style=3D"background-color: rgb(255, 2= 55, 255); "><br></span></div><div><span class=3D"Apple-style-span" style=3D= "background-color: rgb(255, 255, 255); ">Also, both the tension and the amo= unt of collagen in the basilar membrane changes with longitudinal location.= </span></div> <div><span class=3D"Apple-style-span" style=3D"background-color: rgb(255, 2= 55, 255); "><br></span></div><div><span class=3D"Apple-style-span" style=3D= "color: rgb(34, 34, 34); font-family: arial, verdana, helvetica, sans-serif= ; font-size: 12px; line-height: 18px; background-color: rgb(242, 242, 242);= ">Naidu, R.C. and Mountain, D.C. (2007) Basilar membrane tension calculati= ons for the gerbil cochlea. J. Acoust. Soc. Am. 121:994-1002=A0</span><a hr= ef=3D"http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/publi= cations/journal/NaiduMountain2007.pdf" style=3D"margin-top: 0px; margin-rig= ht: 0px; margin-bottom: 0px; margin-left: 0px; padding-top: 0px; padding-ri= ght: 0px; padding-bottom: 0px; padding-left: 0px; border-top-width: 0px; bo= rder-right-width: 0px; border-bottom-width: 1px !important; border-left-wid= th: 0px; border-style: initial; border-color: initial; outline-width: 0px; = outline-style: initial; outline-color: initial; font-size: 12px; font-famil= y: arial, verdana, helvetica, sans-serif; vertical-align: baseline; color: = rgb(80, 147, 177); border-bottom-style: dotted !important; border-bottom-co= lor: rgb(204, 204, 204) !important; text-decoration: none; line-height: 18p= x; text-align: left; background-color: rgb(242, 242, 242); ">[PDF]</a></div= > <div><span class=3D"Apple-style-span" style=3D"background-color: rgb(255, 2= 55, 255); "><br></span></div><div><span class=3D"Apple-style-span" style=3D= "background-color: rgb(255, 255, 255); ">In the case of the gerbil, the BM = dimensions vary in a manner contrary to the conventional wisdom. =A0With th= e exception of the hook region, the width of the basilar membrane changes l= ittle from base to apex and actually increases in thickness from base to ap= ex. =A0On the other hand, in cetaceans, the width and thickness vary signif= icantly from base to apex much as one would expect if the material properti= es were uniform and the beam equation applies.<br> </span><br><div class=3D"gmail_quote">On Fri, Nov 11, 2011 at 6:35 AM, <a h= ref=3D"mailto:reinifrosch@xxxxxxxx">reinifrosch@xxxxxxxx</a> <span dir= =3D"ltr"><<a href=3D"mailto:reinifrosch@xxxxxxxx">reinifrosch@xxxxxxxx= ch</a>></span> wrote:<br> <blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1p= x #ccc solid;padding-left:1ex;"> <div><div><p><font size=3D"2">Hello!</font></p> <p><font size=3D"2">The following is a reaction to an earlier post of this = thread:</font></p> <p><font size=3D"2">As already posted some years ago, it appears possible t= o me that the stiffness S [Newtons per m^3] of the mammalian cochlear basil= ar=A0membrane (BM) decreases=A0by several orders of magnitude from base to = apex. If the elements of the BM are treated as elastic beams, then the foll= owing formula for S is obtained:</font></p> <p><font size=3D"2">S =3D n * Y * (delta-z)^3 / w^4,</font></p> <p><font size=3D"2">where delta-z is the beam thickness, w is the beam leng= th (equal to the BM width), and Y is Young's modulus of the beam materi= al (elasticity modulus, Newtons per m^2); the integer n=A0depends on the wa= y in which the beams are fixed, at their ends,=A0to the walls=A0of the coch= lear channel. If the beams are clamped, then n =3D 60, if not, then n =3D 1= 0.</font></p> <p><font size=3D"2">Fig. 11-73 of von Bekesy's book "Experiments i= n Hearing" (1960) yields a human BM stiffness decrease of only two ord= ers of magnitude=A0from base to apex.=A0Has that experiment been re-done?= =A0</font></p> <p><br><font size=3D"2">Reinhart Frosch,<br>Dr. phil. nat.,<br>CH-5200 Brug= g.<br><a href=3D"mailto:reinifrosch@xxxxxxxx" target=3D"_blank">reinifros= ch@xxxxxxxx</a> .</font><br><br></p> <blockquote><font size=3D"2">----Urspr=FCngliche Nachricht----<br>Von: <a h= ref=3D"mailto:rsran@xxxxxxxx" target=3D"_blank">rsran@xxxxxxxx</a><br= >Datum: 09.11.2011 20:17<br>An: <<a href=3D"mailto:AUDITORY@xxxxxxxx= .CA" target=3D"_blank">AUDITORY@xxxxxxxx</a>><br> Betreff: Re: Laws of physics and old history (A new paradigm?(On pitch and = periodicity (was &quot;correction to post&quot;)))<br><br></font></= blockquote></div></div></blockquote></div><br><br clear=3D"all"><div><br> </div>-- <br><br>David C. Mountain, Ph.D.<br>Professor of Biomedical Engine= ering<br><br>Boston University<br>44 Cummington St.<br>Boston, MA 02215<br>= <br>Email:=A0=A0 <a href=3D"mailto:dcm@xxxxxxxx">dcm@xxxxxxxx</a><br>Website: <= a href=3D"http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/"= >http://www.bu.edu/hrc/research/laboratories/auditory-biophysics/</a><br> Phone:=A0=A0 (617) 353-4343<br>FAX:=A0 =A0=A0 (617) 353-6766<br>Office:=A0 = ERB 413<br><br> </div> --0015174488a2749c6304b1b2941d--