Measurement of cochlear power gain in the sensitive gerbil ear

Abstract

The extraordinary sensitivity of the mammalian ear is commonly attributed to the cochlear amplifier, a cellular process thought to locally boost responses of the cochlear partition to soft sounds. However, cochlear power gain has not been measured directly. Here we use a scanning laser interferometer to determine the volume displacement and volume velocity of the cochlear partition by measuring its transverse vibration along and across the partition. We show the transverse displacement at the peak-response location can be >1,000 times greater than the displacement of the stapes, whereas the volume displacement of an area centred at this location is approximately tenfold greater than that of the stapes. Using the volume velocity and cochlear-fluid impedance, we discover that power at the peak-response area is >100-fold greater than that at the stapes. These results demonstrate experimentally that the cochlea amplifies soft sounds, offering insight into the mechanism responsible for the cochlear sensitivity.

Figure 1. Measurement of the volume displacement

(a) When a tone is presented to the ear, vibrations are measured along and across the basilar membrane through the round window and at the stapes footplates. (b) Magnitude and phase longitudinal and radial patterns of basilar membrane vibration. (c) The relationship between the stapes vibration and the cochlear forward travelling wave. (d) Volume displacement of basilar membrane vibration, measured as the volume bounded by the instantaneous waveform with a maximum displacement centred at the best-frequency location and the in-phase vibrating area on the xy plane (area abcd). The length of this area is a half-wavelength and its width is approximately the basilar membrane width at the best-frequency location. BM, the basilar membrane; BF, best frequency; t_forward, the forward delay; λ, the wavelength. Blue and red colours in panels c and d show the low and high magnitude of the basilar membrane vibration, respectively.

Figure 2. Grouped magnitude and phase data of basilar membrane vibration

(a) The longitudinal magnitude pattern of the basilar membrane response to a 40-dB SPL 16-kHz tone, presented by means (blue solid line) and range of the standard error (red dotted lines) from five cochleae. (b) Corresponding longitudinal phase data. (c) Displacement magnitude as a function of the radial location. Standard errors near the osseous spiral lamina (OSOSL) are smaller than those in the region between 80 to 240 μm due to the relatively high reflectivity. (d) Corresponding radial phase data show little change across the basilar membrane.

Figure 3. Single-point basilar membrane vibration

The magnitude and phase of the basilar membrane vibration were measured at a single longitudinal location as a function of frequency. The ratio of basilar membrane-to-stapes vibration magnitude (BM/stapes) and phase difference between the stapes and basilar membrane are presented in a and b. (a) At 20–60 dB SPL, the magnitude increases with frequency and reaches the maximum at ~16 kHz. The magnitude and sharpness of the peak decreased with the sound level and the peak shifted to low frequencies from ~16 to ~11 kHz (horizontal dotted arrowed line). The magnitude at the peak frequency decreased > 40 dB as the sound level increased from 20 to 90 dB SPL (indicated by vertical dotted arrowed lines). (b) The corresponding phase decreased progressively with frequency. The green curves show the responses at 40 dB SPL, the level used for quantifying the volume displacement in five sensitive cochleae.

Figure 4. Spatial patterns of basilar membrane vibration

Magnitude and phase of the basilar membrane vibration were measured as functions of the longitudinal and radial locations (a–d). The spatial pattern (e) and volume displacement (f) were calculated from the longitudinal and radial data. (a) At low sound levels from 10 to 40 dB SPL, the vibration increases with the distance from the cochlear base and forms a peak at ~2,500 μm. As the stimulus increased ~10,000-fold from 10 to 90 dB SPL, the response peak increased only ~100-fold, from ~0.1 to ~10 nm and shifted towards the base (left). (b) Phase decreased with longitudinal location. The phase slope became flatter at high sound levels. (c) Magnitude as a function of radial location, indicated by the distance from the osseous spiral lamina (OSOSL). The displacement magnitude varied significantly radially. (d) Phase show no significant change across the basilar membrane. Cartoon inset indicates the cross-section of the cochlear partition, with one inner hair cell (left) and three outer hair cells in red. (e) Magnitude spatial pattern of basilar membrane response to a 40-dB SPL 16-kHz tone. (f) Instantaneous waveform of the basilar membrane vibration. Blue and red colours in e and f show the low and high magnitude of the basilar membrane vibration, respectively. (g) Spatial relationship of the quantified half wavelength and the basilar membrane length.

Figure 5. Power gain of basilar membrane vibration

(a) Volume displacements of the basilar membrane (solid line) and stapes (dotted line) vibration as a function of the sound level. (b) Energy input and output functions of the basilar membrane (solid line) and stapes (dotted line) vibration. (c) Point displacements of the basilar membrane (solid line) and stapes (dotted line) vibration. (d) Energy (blue), volume- (red) and point- (black) displacement gains as a function of the sound level. Green circles show energy gains from five sensitive cochleae (mean = 61, s.e. = 11, n = 5).