Transcript 1 - University of Southampton

Modelling random changes in the parameters
along the length of the cochlea and the effect on hearing sensitivity
Emery M.
1
Ku ,
1ISVR,
Stephen J.
1
Elliott ,
Ben
1
Lineton
University of Southampton, UK
Abstract
Linear, Stable Frequency Domain Results
The active cochlea is often modelled as having a uniformly varying distribution of parameters. In a real biological system,
however, uniform distributions will always be disrupted by random spatial variations. In addition, noise-induced damage can be
manifest as severe ‘focal lesions’ in the organ of Corti which compromise the cochlear amplifier in specific regions, thus also
disturbing the smooth variation of parameters. A state space model of the cochlea has been developed that can be used to
investigate the effect of such changes. The frequency responses of cochleae with near-unstable distributions of physical
parameters are determined and compared with audiometric data. The limit cycles that are generated once the system does become
unstable are then compared with measured spontaneous otoacoustic emissions.
Introduction
More than 8% of the population of many developed countries suffer from significant sensorineural hearing loss. In addition,
approximately 90% of all hearing loss in adults is due to cochlear malfunction.1 This is a widespread problem that is only recently
beginning to receive greater attention from scientists modelling cochlear mechanics.
Most researchers agree upon the existence of a Cochlear Amplifier (CA) that actively enhances the response of the travelling
wave as it propagates through the human cochlea. The CA is believed to be driven by the motility of the Outer Hair Cells (OHCs) in
the organ of corti, though the exact mechanism by which the OHCs accomplish this is still a matter of debate.
In this study, the micromechanical feedback gain in a discrete fluid-coupled cochlear model2, which is analogous to the activity
of a local set of OHCs, is randomly perturbed as a function of position. Frequency-domain results are generated from a near-unstable
linear system and compared with measured equal-loudness curves; time-domain results are also generated from an unstable nonlinear
cochlea and compared with measured Spontaneous Otoacoustic Emissions (SOAEs).
Methods
Variations in the micromechanical parameters of cochlear models can result in instability, which invalidates frequency-domain
analysis. A general state space framework has been developed to determine the linear stability of cochlear models.3 Another benefit of
the state space formulation is that it readily allows the model to be simulated in the time-domain. In order to produce an output
pressure in the ear canal that can be compared with SOAE measurements, a two-port model of the middle and outer ears is
incorporated into the model.
The complete time-domain analysis involves three steps, which are illustrated below:
1) taking an input volume velocity in the ear canal, Qe  t , to produce an output acceleration at the stapes, wc  t ;
2) this acceleration, wc  t  , then becomes the input to a nonlinear time domain simulation of the cochlea that produces an output
pressure at the round window, Pc(t);
3) Pc(t) is used to generate Pe(t), the output pressure in the ear canal that can be compared with SOAEs.
1)
2)
Figure 5
Basilar Membrane (BM) velocity responses
given a near-unstable distribution of gains at
several nominal gain levels.
Figure 6
Inverse BM velocity of data presented in previous
figure, now plotted against characteristic
frequency.
Frequency [Hz]
Figure 7
Measured equal loudness curves.4
Nonlinear, Unstable Time Domain Results
These results were generated
from a single unstable cochlea; the
poles of this system are shown in
Figure 8.b.
A pulse was directly fed in
to the simulation, (see Methods,
2). The spectrum of the output
pressure in the cochlea was
transformed to obtain the ear canal
pressure (see Methods, 3), which
is plotted in Figure 8.a.
20ms were simulated using
MATLAB’s ode solver, ode45,
given an output sampling rate of
100kHz.
The spectra of the
generated SOAEs are comparable
to human measurements, such as
the data shown in Figure 9.
Figure 9
Measured human SOAEs in one ear.5
Figure 8.a-b
Response of an unstable nonlinear cochlea: a) pressure in the ear
canal; b) detailed view of pole positions: the solid red line
represents the boundary of stability, unstable poles are circled.
Conclusions and Future Work
The trends in the frequency domain analysis show good agreement with the equal loudness curves. Additionally,
there is a regular spectral periodicity of the peaks in the frequency domain analysis, analogous to that observed in
stimulus-frequency OAEs. This also occurs in the spacings of unstable poles, which agree with predictions.6 This will be
the subject of a future publication.
3)
Figure 4
Nonlinear, micromechanical
model.3
Figures 1-4
Steps involved in the time-domain simulation of the
nonlinear cochlea: from input volume velocity, Qe, to
output ear canal pressure, Pe.
The SOAE spectrum obtained from the unstable cochlea shows good agreement with the stability analysis.
However, distinct peaks at near-unstable frequencies and wider-than-expected bandwidths at unstable frequencies imply
that transients are being included in the analysis. In order to cleanly resolve SOAEs, longer simulations are required.
References
1
Jesteadt, W. (Editor) (1997). Modeling Sensorineural Hearing Loss. Hillsdale, NJ: Erlbaum.
4
Mauerman et al, (2004). Fine structure of the hearing threshold and loudness perception. J.
Acoust. Soc. Am. 116 (1070)
2
S.T. Neely, D.O. Kim, (1986). A model for active elements in cochlear biomechanics. J. Acoust.
Soc. Am. 79(5)
5
Martin et al, (1990). Distortion product emissions in humans. I. Basic properties in normally
hearing subjects., Ann Otol Rhinol Laryngol Suppl 147 (3-14).
3
S.J. Elliott, E.M. Ku, B. Lineton, (2007). A state space model for cochlear mechanics.
Manuscript accepted for publication by J. Acoust. Soc. Am on 14th Aug, 2007.
6 G.
Zweig and C.A. Shera, (1995). The origin of periodicity in the spectrum of emissions. J.
Acoust. Soc. Am. 98 (4).