Experimental Study of Vibrations of Gerbil Tympanic Membrane with Closed Middle Ear Cavity

Abstract

The purpose of the present work is to investigate the spatial vibration pattern of the gerbil tympanic membrane (TM) as a function of frequency. In vivo vibration measurements were done at several locations on the pars flaccida and pars tensa, and along the manubrium, on surgically exposed gerbil TMs with closed middle ear cavities. A laser Doppler vibrometer was used to measure motions in response to audio frequency sine sweeps in the ear canal. Data are presented for two different pars flaccida conditions: naturally flat and retracted into the middle ear cavity. Resonance of the flat pars flaccida causes a minimum and a shallow maximum in the displacement magnitude of the manubrium and pars tensa at low frequencies. Compared with a flat pars flaccida, a retracted pars flaccida has much lower displacement magnitudes at low frequencies and does not affect the responses of the other points. All manubrial and pars tensa points show a broad resonance in the range of 1.6 to 2 kHz. Above this resonance, the displacement magnitudes of manubrial points, including the umbo, roll off with substantial irregularities. The manubrial points show an increasing displacement magnitude from the lateral process toward the umbo. Above 5 kHz, phase differences between points along the manubrium start to become more evident, which may indicate flexing of the tip of the manubrium or a change in the vibration mode of the malleus. At low frequencies, points on the posterior side of the pars tensa tend to show larger displacements than those on the anterior side. The simple low-frequency vibration pattern of the pars tensa becomes more complex at higher frequencies, with the breakup occurring at between 1.8 and 2.8 kHz. These observations will be important for the development and validation of middle ear finite-element models for the gerbil.

Appendix

An inset in Figure 8 shows the Nyquist plots for three anterior beads in the frequency range of 3,078 to 4,922 Hz, as an example of their use for verification of the phase response as mentioned in the “Measurement and analysis procedures” section. The unwrapped phases shown for these three beads follow what the Nyquist plots display regarding the phase evolution, which can be described in terms of “phasors,” that is, vectors drawn from the origin to points on the Nyquist plot. When for increasing frequency the phasor rotates clockwise, the phase angle decreases (becomes more negative), and vice versa. All three curves start in the same quadrant and end in that same quadrant, but the trajectories in between are quite different. At the beginning of the violet trajectory on the Nyquist plot, the phasor rotates clockwise through a small angle then counterclockwise, corresponding to a phase decrease up to about 3,300 Hz and then a phase increase up to about 3,650 Hz. After this frequency, it rotates clockwise, which corresponds to a decrease in phase up to a point where the phasor becomes extremely short and the trajectory becomes almost tangent to the real axis, at about 4,100 Hz. Approaching and passing this tangent zone, with the phasor still rotating clockwise and encircling the origin, causes a sharp drop in the phase plot, after which the phasor becomes longer and continues to rotate clockwise, corresponding to a smooth phase drop. (When the phasor becomes very short, a very small difference in the real or imaginary parts due to noise or frequency resolution can change whether it encircles the origin or not, which in turn causes a difference of 360 ° in the phase.) The phasors for the blue and gray trajectories start rotating clockwise and both of them make circles, but the gray trajectory encircles the origin while the blue trajectory does not. This corresponds to a continuous drop of the gray phase plot, but an increase at about 4 kHz in the blue phase plot.