Two-tone distortion at different longitudinal locations on the basilar membrane

Abstract

When listening to two tones at frequency f1 and f2 (f2>f1), one can hear pitches not only at f1 and f2 but also at distortion frequencies f2-f1, (n+1)f1-nf2, and (n+1)f2-nf1 (n=1,2,3...). Such two-tone distortion products (DPs) also can be measured in the ear canal using a sensitive microphone. These ear-generated sounds are called otoacoustic emissions (OAEs). In spite of the common applications of OAEs, the mechanisms by which these emissions travel out of the cochlea remain unclear. In a recent study, the basilar membrane (BM) vibration at 2f1-f2 was measured as a function of the longitudinal location, using a scanning laser interferometer. The data indicated a forward traveling wave and no measurable backward wave. However, this study had a relatively high noise floor and high stimulus intensity. In the current study, the noise floor of the BM measurement was significantly decreased by using reflective beads on the BM, and the vibration was measured at relatively low intensities at more than one longitudinal location. The results show that the DP phase at a basal location leads the phase at an apical location. The data indicate that the emission travels along the BM from base to apex as a forward traveling wave, and no backward traveling wave was detected under the current experimental conditions.

Fig. 1

Magnitude (A) and phase (B) responses at 2f1-f2 in a sensitive cochlea (solid lines) and an insensitive cochlea (dotted lines), and the magnitude and phase transfer functions at different sound pressure (panels C and D). Data were measured from the same longitudinal location. Dramatic difference between the results in the sensitive preparation and those under post-mortem conditions show that the observed emission response of the BM is closely related to cochlear sensitivity. The magnitude response peaks at 2f1-f2 in panel A are very similar to the BF (15 kHz) shown in panel C.

Fig. 2

Magnitude and phase responses of the BM as a function of the 2f1-f2 frequency from two longitudinal locations. Panels A and B are measured from the apical bead, and panels C and D are from the basal bead. The distance between the beads is 109 μm. In panels A and C, across different intensities, the vibration magnitude increases with 2f1-f2, reaching a maximum where 2f1-f2 approaches f2 or 2f1/f2 is close to one. In panel A, at frequencies near f2, the separation between the curves is significantly smaller than the intensity increment of 10 dB, revealing a nonlinear growth. Phase-frequency curves in Fig. 2B and D show negative slopes. Above 10 kHz, the phase shows a linear relationship to the 2f1-f2 frequency.

Fig. 3

Magnitude and phase transfer functions of the BM measured at 30 dB SPL from same two longitudinal locations as for data in Fig. 2. The arrows in panel A show the relationship between the f2 and the BFs. Panel A shows that BFs of two locations are approximately 17.0 kHz for the apical bead (solid line) and 18.5 kHz for the basal bead (dotted line). The phase transfer function in panel B shows that for a given frequency the phase of the basal bead leads the phase of the apical bead, which indicates a forward traveling wave.

Fig. 4

Magnitude and phase comparison between the apical bead (solid lines) and basal bead (dotted lines) responses at different intensities. The patterns of magnitude response across intensities are very similar while response of the apical bead is significantly greater than that of the basal bead. Because of the dominating magnitude responses and linear phase behavior at frequencies above 10 kHz, the group delay was calculated at frequencies above 10 kHz. The phase slopes show that at a given intensity, the group delay of the apical-bead location is greater than that at the basal location. For a given location, the group delay decreases with intensity.

Fig. 5

Magnitude and phase responses of the BM as a function of the 2f1-f2 frequency from two different longitudinal locations with a separation of ~366 μm. Data are similar to those in Fig. 2 but are from a different animal. In panels A and C, magnitude increases with 2f1-f2, with a maximum at the high frequency side indicating that these observed locations are at or basal to the f2 place. Data in this figure are very similar to those in Fig. 2, except for a greater difference in phase slope in panels B and D than in Figs. 2B and 2D.

Fig. 6

Magnitude and phase transfer functions of the BM measured at 30 dB SPL from the same two longitudinal locations as for data in Fig. 5. The arrows in panel A show the relationship between the f2 and the BFs. The BFs of two locations are approximately 14 kHz for the apical bead (solid line) and 19 kHz for basal bead (dotted line) shown in panel A. The phase transfer function in panel B shows that the phase of the basal bead leads the phase of the apical bead, indicating a forward traveling wave.

Fig. 7

Comparison between the apical bead (solid lines) and basal bead (dotted lines) responses at different intensities. The phase slopes also show that the delay of the apical bead is greater than the basal-bead delay. Thus, panels B, D, and F are also consistent with a forward traveling wave at the emission frequency.

Fig. 8

Delay difference (A) and traveling wave velocity (B) as a function of the distance between the beads. Data were derived from the phase values of two beads at two longitudinal locations in six animals. Positive delays from a basal location to an apical location in panel A indicate forward propagation. Most velocity values are between 1 to 10 m/s.