Two-dimensional cochlear short-wave model. ("reinifrosch@xxxxxxxx" )

Subject: Two-dimensional cochlear short-wave model.
From:    "reinifrosch@xxxxxxxx"  <reinifrosch@xxxxxxxx>
Date:    Sun, 3 Feb 2008 11:56:33 +0000

Dear List Members, In recent calculations of phases of distortion-products (DP's) and DP oto-acoustic emissions (DPOAE's) in mammalian cochleae I have obtained fairly good agreement with measured phases by means of the two-dimensional short-wave cochlear model; see, e.g., Eq. (23) of "Ranke revisited -- a simple short-wave cochlear model" by W. M. Siebert (1974), JASA 56, 594-600. Here I would like to point out that according to my (hopefully correct) interpretation of this model the radius r of the approximately half-circle-shaped "wavy" liquid zones on both sides of the basilar membrane (BM) in the real cochlea depends on the BM width. First case: Local wave number of travelling surface wave: k = 2pi / wavelength = 1000 m^-1; thickness of liquid layers with significant water-particle motion (on circular trajectories): delta-z = 1/k = 1 mm; BM-width: w = 0.1 mm; half-channel cross section: q_hc = 1 mm^2; therefore effective half-channel height H = q_hc / w = 10 mm; short-wave condition is fulfilled: Hk = 10 >> 1; cross section of wavy liquid zones: q_wz = w * delta-z = 0.1 mm^2; radius of half-circle-shaped wavy zone in real cochlea: r = sqrt(2q_wz / pi) = 0.25 mm. Second case: As first case, but w = 0.2 mm; therefore H = 5 mm; Hk = 5 >> 1; short-wave condition is still fulfilled; q_wz = 0.2 mm^2; r = 0.36 mm, greater than in first case. With best wishes, Reinhart Frosch. Reinhart Frosch, Dr. phil. nat., r. PSI and ETH Zurich, Sommerhaldenstr. 5B, CH-5200 Brugg. Phone: 0041 56 441 77 72. Mobile: 0041 79 754 30 32. E-mail: reinifrosch@xxxxxxxx .

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Electrical Engineering Dept., Columbia University