Fig 1.
Middle-ear (ME) and basilar membrane (BM) vibrations evoked by acoustic clicks.
The drawing at the top of panel (A) represents an uncoiled cochlea, whose length equals the mean value reported by [14]. The three plots at the bottom of panel (A), from left to right, represent stapes, BM at location 1 (CF = 16 kHz) and BM at location 2 (CF = 6 kHz) responses to 95-dB pSPL condensation clicks. Locations 1 and 2 are at a scale, following equations by [14]. Panel (B) exhibits velocity profiles of stapes and BM (locations 1 and 2) responses to 95-dB pSPL clicks. Waveforms displaying BM responses are shown inverted. Both original and shifted (4-μs) versions of the stapes responses are shown in (B). Inset in panel (B) displays in semi-logarithmic coordinates absolute values of the responses in main panel. Panel (C) displays phase-vs.-frequency functions from the click responses at locations 1 and 2. Phase functions were normalized relative to stapes (continuous lines) or umbo (dashed lines) motion. Continuous red lines in panel (C) represent linear fits to the phase-vs.-frequency segments indicated by the red lines. Negative numbers next to each red line represent the slope of each linear fit.
Fig 2.
Onsets of stapes and BM responses to clicks are similar.
Panels (A) and (C) display umbo, stapes and BM responses to clicks in the animal preparation indicated in each panel. Data are expressed in velocity units and BM responses are shown inverted. Stapes responses (gray lines) have been delayed by 4 μs. Continuous black lines with circles represent BM click response at the maximum possible level, as indicated in each panel. Dotted dashed lines display BM responses to clicks at the maximum level minus 10 dB. Insets in (A) and (B) display absolute values of stapes and BM responses in semi-logarithmic coordinates. Circles in the insets represent the so-called initial segment (see text). Black lines in (B) and (D) display phase-vs.-frequency curves, φ(2πf), of the responses in (A) and (C), respectively. Red trace in (D) represents a φ(2πf) measured from responses at another BM location in the same animal. Inset in (D) displays a local phase-vs.-frequency function equal to φ2(2πf) − φ1(2πf) [21].
Fig 3.
Panel (A) displays plots of φ(2πf), obtained from BM responses to clicks at three locations along the same cochlea. Two local phase functions obtained from the phase functions in (A) are shown in panel (B).
Fig 4.
Panel (A) displays h(t) functions obtained from middle ear (stapes or umbo) and BM responses to 95-dB pSPL clicks. The thickest lines in (B) were computed from responses to 95-dB pSPL clicks (the waveform is the same plotted in panel (A)); the remaining lines from responses to 85-, 75- and 65-dB pSPL clicks. All the traces in panel (B) were obtained using the umbo response as input. Upper insets in (A) and (B) show the initial part of the h(t) functions displayed in the main panels. Symbols in the inset in panel (B) represent the four initial samples of the gain functions. Panel (C) displays one h(t) function (black line) from panel (A) (95-dB pSPL) as well as a synthetized version (gray line) of it (see Eq 2 in Methods section). The blue line with symbols in the lower inset in panel (A) represents h(t) function evaluated after delaying the input waveform by 5 samples (see main text). The red line with symbols in the same inset is the same as the one shown in the upper inset (same color). Panel (D) exhibits the instantaneous frequency representation of the gain function in panel (A) (red line).
Fig 5.
h(t) functions at several cochlear locations.
Gain functions were computed from BM and umbo responses to clicks at four intensity levels. Results in (A) and (B) originate from data recorded at two location in the same cochlea. (Likewise for results in (C) and (D).) CFs and stimulus levels are shown in each panel. Insets display fragments of each gain function, from -20 to 20 μs. Red filled circles in each panel represent the average of each set of four h(t).
Fig 6.
Gain function without frequency plateau.
Panel (A) displays the original gain function (red lines) and the modified version (black lines) of the original waveform (see main text). The inset in panel (A) shows the onset of both gain functions. Modification of the original phase function was achieved by replacing the plateau with phase values having a group delay of 1.08 ms (black line in (B)). Original amplitude plateaus (red line in inset in (A)) were replaced with values that decrease at a slope of -51 dB per octave.