View of the left side of a gerbil head showing the locations of measurement access holes and the view of the stapes through the posterior hole used for most stapes velocity measurements. The skin and soft tissue were removed from the superior and lateral aspects of the auditory bulla. A brass sound coupler was cemented about the opening of the bony ear canal (EC). A hole was made in the bulla wall posterior to the bony EC (“posterior hole”). A retroreflective target (gray square) was placed on the stapes posterior crus (PC). The view of the stapes was limited by the tympanic annulus (TA), the horizontal semicircular canal (HSC), and the stapedial artery (SA). At MEEI, stapes velocity was measured from a direction as close to the piston direction (dot-dashed line) as possible. The angle between the measurement direction (the baseline direction, thick gray line) and the piston direction (labeled ) was 27°–37°. (Note that angles are foreshortened in this view and appear larger or smaller than they actually were.) At Bristol, this hole was larger, and between this baseline measurement direction and the piston direction (labeled ) was approximately 47°. Another hole (“superior hole”) was made in the bulla superior to the posterior hole to vent the ME and (in some bones) to provide an alternate view of the posterior crus target for stapes velocity measurements: for this measurement direction (solid and dashed gray line, labeled ) was 61°–65°.
(a) Transfer admittance with the probe tube at various locations along an approximately longitudinal trajectory. Legend indicates the approximate distance from the probe tube tip to a point on the TM over the umbo. Top: magnitude; bottom: phase. (b) with the probe tube at the various locations. The relative invariance of with probe tube location below shows that variations in with probe tube location are due primarily to variations in among those locations. Also shown is a typical measurement noise floor (gray dots). Top: magnitude; bottom: phase relative to with the probe tube approximately from the umbo.
Ratios of sound pressure near the umbo to sound pressure in the bony EC at various distances from the umbo. Each curve is the mean (in dB) of measurements in four ears. Top: magnitude ratio in dB; bottom: phase difference. At the bottom of each panel is the s.d. (right-hand vertical scale). in the other 15 ears (see Figs. 5 and 6) was corrected by the mean curve corresponding to the measurement location in that ear.
Mean in four ears at MEEI in which was measured, shown in the experimental reference frame of the vibrometer. Each curve is the logarithmic mean of 11–22 measurements normalized by . Top: magnitude; bottom: phase. At the bottom of each panel is the s.d. (right-hand vertical scale). The dip and ripple near are due to a resonance between the compliance of the air in the bulla and the mass of the bulla hole. (a) Logarithmic frequency scale; (b) linear frequency scale. The thin dashed line in panel (a) shows a log-log slope of . The thin dashed line in panel (b) indicates the phase slope corresponding to a 20–μs delay.
Mean in nine ears at MEEI in which was measured from the umbo (black lines), corrected by a curve from Fig. 3. Each curve is the logarithmic mean of two to six measurements. in the four ears in Fig. 4 is shown by gray lines. An outlier (0309L) is shown by a dashed line. Top: magnitude; bottom: phase. (a) Logarithmic frequency scale; (b) linear frequency scale. The thin dashed line in panel (b) indicates the phase slope corresponding to a 25–μs delay.
of in 6 ears at Bristol (black line, error bars) and 13 ears at MEEI (gray line, shading). Top: magnitude; bottom: phase. (a) Logarithmic frequency scale; (b) linear frequency scale. The dashed line indicates the phase slope corresponding to a delay.
in a representative ear (0306L) at MEEI with the inner ear intact (solid line), with the round window punctured and open (dashed line), and with the inner ear drained (dot-dashed gray line). Results in two other MEEI ears were similar. Top: magnitude; bottom: phase.
Variations in with measurement direction. (a) Magnitude ratios (top) and phase differences (bottom) for a typical ear at Bristol as the measurement direction was varied from the baseline direction through goniometer angles and about longitudinal and transverse axes, respectively (see Sec. II B). Effects of various (which correspond approximately to changes in the angle between the measurement direction and the piston direction) are shown as solid and long-dashed lines; effects of various (which had little effect on ) are shown by dotted lines. The range of measurements from the baseline direction is shown by the shading. (b) Ratio of measured through the superior vs posterior bulla holes in three ears at MEEI. Top: magnitude ratio; bottom: phase difference.
(Color online) Reconstructed Lissajous figures of the displacement of the stapes posterior crus target (normalized by frequency) at several frequencies in three dimensions in an intrinsic reference frame aligned with the stapes (insets) from one right ear (ubg17) at Bristol; two other ears (one left, one right) were similar. (a) Looking in the direction (approximately anterior); (b) looking in the direction (from the stapes head into the cochlea); (c) looking in the direction (approximately superior).
Ratio of transverse to pistonlike stapes motion. (a) (black lines and filled symbols) and (gray lines and open symbols) in three ears at Bristol (in the intrinsic reference frame), where is the motion in the piston direction. (b) in three ears at MEEI, where is the direction in the measurement plane (defined by the two measurement directions) closest to the piston direction and is in the orthogonal direction. The legend indicates the angle between and . Noisy data at are omitted. Top: magnitude ratio; bottom: phase difference.
, the ratio of measured to the piston component , in three ears at Bristol in the intrinsic reference frame. The dot-dashed line is the cosine of the angle (, shading) between the measurement direction and the axis. Top: magnitude; bottom: phase.
Comparison of our mean (shaded area) to previously published measurements: Rosowski et al. (1999) (logarithmic mean; “Ros. et al.;” dotted); Overstreet and Ruggero (2002) (median; “O. & R.;” gray line), de la Rochefoucauld et al., 2008 (in piston direction; linear mean; “de la R. et al.;” dashed), and Decraemer et al., (2007) (piston, computed in an intrinsic reference frame; logarithmic mean; “Decr. et al.;” dot-dashed). Top: magnitude; bottom: phase. (a) Logarithmic frequency scale; (b) linear frequency scale.
Comparison of our mean (thick black line; left axis) to the mean scala vestibuli pressure gain described by Olson (2001) (shading; right axis). Top: magnitude; bottom: phase. The relative positions of the left and right magnitude axes were chosen for the closest alignment of midfrequency and .
Cochlear input impedance (thick black line) computed from the mean and in Fig. 13. Top: magnitude; bottom: phase angle. Dotted lines indicate limits of for a passive system. S.d of (not shown) is about a factor of 12; s.d. of is shown by shading. Also shown are in three ears by Decraemer et al. (2007, gray lines, phase-wrapped as suggested in that publication) and the mean in five ears by de la Rochefoucauld et al., 2008, dashed line).
Sound pressure at the umbo required to produce a constant level of cochlear input across frequency. Shown are that produces a constant stapes velocity of (equivalent to a constant stapes volume velocity of ) (black line) and that provides a constant cochlear sound power input of (solid gray line, only at frequencies where is positive). Also shown is for computed by assuming that is purely resistive (dashed gray line). The mean gerbil audiogram (Ryan, 1976) is shown by the dotted line and squares. (a) Logarithmic frequency scale; (b) linear frequency scale.
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