chapter 36 - Vestibular Mechanics - KEMT FEI TUKE

36.5 Otolith Frequency Response
© 2000 by CRC Press LLC
(36.10)
This transfer function can now be studied in the frequency domain. It should be noted that these are
linear partial differential equations and that the process of frequency domain analysis is appropriate. The
range of values of ε = 0.01–0.2, M = 5–20, and R = 0.75 have been established by Grant and Cotton
[1991] in a numerical finite difference solution of the governing equations. With these values established,
the frequency response can be completed.
In order to construct a magnitude- and phase-versus-frequency plot of the transfer function, the
nondimensional time will be converted back to real time for use on the frequency axis. For the conversion
to real time the following physical variables will be used: ρ o = 1.35 g/cm 3 , b = 15 µm, µ f = 0.85 mPa·s.
The general frequency response is shown in Fig. 36.4. The flat response from DC up to the first corner
frequency establishes this system as an accelerometer. These are the range-of-motion frequencies encountered
in normal motion environments where this transducer is expected to function.
The range of flat response can be easily controlled with the two parameters ε and M. It is interesting
to note that both the elastic term and the system damping are controlled by the gel layer, and thus an
animal can easily control the system response by changing the parameters of this saccharide gel layer.
The cross-linking of saccharide gels is extremely variable, yielding vastly different elastic and viscous
properties of the resulting structure.
The otoconial layer transfer function can be compared to recent data from single-fiber neural recording.
The only discrepancy between the experimental data and theoretical model is a low-frequency phase lead
and accompanying amplitude reduction. This has been observed in most experimental single-fiber
recordings and has been attributed to the hair cell.
(f)
FIGURE 36.3 (continued)
Vs
A =− g x
t
∂
∂ −
⎛ ⎞
⎜ ⎟
⎝ ⎠