Question on human cochlear-partition stiffness. ("reinifrosch@xxxxxxxx" )


Subject: Question on human cochlear-partition stiffness.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Fri, 25 Nov 2011 18:40:40 +0000
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

------=_Part_3910_2497668.1322246440008 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Dear colleagues, Please permit me one more posting on the stiffness S of the human CP [CP = =3D cochlear partition =3D basilar membrane (BM) and cells attached to the = BM; S =3D spring constant per CP surface unit, Newtons per metre-cubed]. = =20 According to the left ordinate scale of Fig. 11-73 of "Experiments in Heari= ng" by von Bekesy, the volume change per millimetre of length at distance-f= rom-base x =3D 3 mm at an across-CP pressure difference of 1 cm of water is= 7 * 10^-8 cm^3. For the local CP width of 0.15 mm, that translates into th= e following CP stiffness: =20 S(3 mm) =3D 2.1 * 10^8 N/m^3. (1) =20 If, however, the human CP stiffness is assumed to be as defined by Eq. (3.2= .1) and by the caption of Fig. 5.2 of de Boer's chapter in the book "The Co= chlea" (1996), then one obtains =20 S(3 mm) =3D 4.1 * 10^9 N/m^3, (2) =20 greater than the value in Eq. (1) by a factor of almost twenty. A possible explanantion can be found with the help of Fig. 2.3B of Slepecki= 's chapter in "The Cochlea" (1996): The boundary, made by tight junctions, = between perilymph and endolymph is not the BM, but rather the RL (reticular= lamina) and the scala-media-side walls of the Hensen and Claudius cells. A= ccording to Figs. 11-71 and 11-72 of "Experiments in Hearing", the pressure= in the scala tympani was reduced below the pressure in air and in scala ve= stibuli. According to the right scale of Fig. 11-73 and to the text above t= hat diagram (maximum displacement 0.01 mm), the pressure difference delta-p= applied for the measurement at x =3D 3 mm was as high as ~100 cm of water.= The change from delta-p =3D 0 to delta-p =3D 100 cm of water was slow, so = the (comparatively low) scala-tympani pressure presumably penetrated upward= s through the BM, and up to the mentioned cell walls. Therefore Fig. 11-73 = may show the stiffness of those cell walls, rather than that of the CP. Our= Eq. (2), in contrast, gives the effective CP stiffness (across-CP pressure= difference divided by displacement of the centre-of-mass of the local CP s= lice) valid at audio-frequency pressure oscillations. Question to biologists: Do you agree with that (very preliminary) explanati= on? Reinhart Frosch, CH-5200 Brugg. reinifrosch@xxxxxxxx . ------=_Part_3910_2497668.1322246440008 Content-Type: text/html;charset="UTF-8" Content-Transfer-Encoding: quoted-printable <html><head><style type=3D'text/css'> <!-- div.bwmail { background-color:#ffffff; font-family: Trebuchet MS,Arial,Helv= etica, sans-serif; font-size: small; margin:0; padding:0;} div.bwmail p { margin:0; padding:0; } div.bwmail table { font-family: Trebuchet MS,Arial,Helvetica, sans-serif; f= ont-size: small; } div.bwmail li { margin:0; padding:0; } --> </style> </head><body><div class=3D'bwmail'><P><FONT size=3D2>Dear colleagues,</FONT= ></P> <P><FONT size=3D2>Please permit me one more&nbsp;posting on the stiffness S= of the human CP [CP =3D cochlear partition =3D basilar membrane (BM) and c= ells attached to the BM; S =3D spring constant per CP surface unit, Newtons= per metre-cubed].&nbsp;&nbsp;</FONT></P> <P><FONT size=3D2>According to the left ordinate scale of Fig. 11-73 of "Ex= periments in Hearing" by von Bekesy, the volume change per millimetre of le= ngth at distance-from-base x =3D 3 mm at an across-CP pressure difference o= f 1 cm of water is 7 * 10^-8 cm^3. For the local CP width of 0.15 mm, that = translates into the following CP stiffness:</FONT></P> <P><FONT size=3D2></FONT>&nbsp;</P> <P><FONT size=3D2>S(3 mm) =3D 2.1 * 10^8 N/m^3.&nbsp;&nbsp;&nbsp;&nbsp; (1)= </FONT></P> <P><FONT size=3D2></FONT>&nbsp;</P> <P><FONT size=3D2>If, however,&nbsp;the human CP stiffness is assumed to be= as defined by Eq. (3.2.1) and by the caption of Fig. 5.2 of de Boer's chap= ter in the book "The Cochlea" (1996), then one obtains</FONT></P> <P><FONT size=3D2></FONT>&nbsp;</P> <P><FONT size=3D2>S(3 mm) =3D 4.1 * 10^9 N/m^3,</FONT><FONT size=3D2>&nbsp;= &nbsp;&nbsp;&nbsp; (2)</FONT></P> <P><FONT size=3D2></FONT>&nbsp;</P> <P><FONT size=3D2>greater than the value in Eq. (1) by a factor of almost t= wenty.</FONT></P> <P><FONT size=3D2>A possible explanantion can be found with the help of Fig= . 2.3B of Slepecki's chapter in "The Cochlea" (1996): The boundary, made by= tight junctions, between perilymph and endolymph is not the BM, but rather= the RL (reticular lamina) and the scala-media-side walls of the Hensen and= Claudius cells. According to Figs. 11-71 and 11-72 of "Experiments in Hear= ing",&nbsp;the pressure in the scala tympani was reduced below the pressure= in air and in scala vestibuli. According to the right scale of&nbsp;Fig. 1= 1-73 and to the text above that diagram (maximum displacement 0.01 mm), the= pressure difference delta-p applied for the measurement at x =3D 3 mm was = as high as ~100 cm of water. The change from delta-p =3D 0&nbsp;to delta-p = =3D 100 cm of water was slow, so the (comparatively low) scala-tympani pres= sure presumably penetrated upwards through the BM, and up to the mentioned = cell walls.&nbsp;Therefore Fig. 11-73 may show the stiffness of those cell = walls, rather than that of the CP. Our Eq. (2), in contrast, gives the effe= ctive&nbsp;CP stiffness (across-CP pressure&nbsp;difference divided by disp= lacement of the centre-of-mass of the local CP slice) valid at audio-freque= ncy pressure oscillations.</FONT></P> <P><FONT size=3D2>Question to biologists: Do you agree with that (very prel= iminary) explanation?<BR></FONT><BR><FONT size=3D2>Reinhart Frosch,<BR>CH-5= 200 Brugg.<BR>reinifrosch@xxxxxxxx . </FONT></P></div></body></html> ------=_Part_3910_2497668.1322246440008--


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