Transcript - ePrints Soton

Does the Human Cochlea Work like a Laser?
Emery M. Ku
ISVR, University of Southampton, UK
[email protected]
Abstract
Nonlinear, Unstable Time Domain Results
The sharply tuned sense of hearing in humans is believed to be due to active amplification in the cochlea. One seemingly
natural consequence of this ‘cochlear amplifier’ is the existence of spontaneous otoacoustic emissions (SOAEs), narrow-band
tones that are detected in the ear canals of 33% to 70% of all normal-hearing individuals.1 The mechanisms underlying the
features and generation of SOAEs have long been a subject of debate. Zweig and Shera2 argue that SOAEs are created by
multiple travelling-wave reflections between the middle ear boundary and a dense array of inhomogeneities scattered throughout
the cochlea; Shera3 likens this process to activity in a laser cavity. This theory is contrary to previous ideas which assume
independently unstable oscillators in the cochlea.
The cochlear model was determined to be unstable at 2kHz given the step-change in gain as a function of
position shown in Figure 2. The nonlinear time domain simulation, shown in Figure 4, illustrates the forward
travelling wave generated by the initial click at t=0, and also backward-travelling waves reflected off of the
inhomogeneity at x = 16.3 mm. Figures 4 and 6 show the analogy between a laser and the cochlea, respectively.
This work uses a state space formulation of the cochlea to test the predictions made by Zweig and Shera2. The Elliott et al.
model of the cat cochlea4 has been revised to describe characteristics of the human cochlea. Linear instabilities arise across a
wide bandwidth of frequencies when the smooth spatial variation of basilar membrane impedance is disturbed. The salient
features of Zweig and Shera’s theory2 are observed in this active model given perturbations in the distribution of feedback gain
along the cochlea. A step change in gain is used to demonstrate system instability.
Figure 4
Simplified diagram of a typical laser.
Figure 6
Simplified diagram of a cochlea..
Output mirror,
Mostly reflective
Middle Ear,
Mostly reflective
Back mirror,
Fully reflective
Cochlear
Inhomogeneity,
Slightly reflective
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 model6 is perturbed as a function of
position. Time-domain results are also generated from an unstable nonlinear cochlea and its attributes compared with a typical laser.
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.4 Another benefit of the state space formulation is that it readily allows the
model to be simulated in the time-domain. Figures 1-3 illustrate the cochlear model, which approximates the
organ by assuming a one-dimensional set of fluid-coupled elements.
Figure 5
Time domain simulation of the response of a nonlinear cochlea to an impulse at the base.
Basilar membrane velocity is shown as a function of time and position along the cochlea.
A black line at 16.3 mm marks the location of the step change in micromechanical gain.
Monochromatic
light output
Micromechanical Feedback Gain vs Position
1.05
0.95
0.85
0
5
10
15
20
25
30
Position along the cochlea [mm]
Figure 2
A step inhomogeneity in the micromechanical gain disturbs the
smooth variation of cochlear impedance as a function of
position in the cochlea.
35
Figure 3
This nonlinear,
micromechanical model3
approximates the motion of
the basilar membrane (M1),
tectorial membrane (M2),
and OHC activity (γZ4).
2.
3.
Talmadge, C.L., Long, G.R., Murphy, W.J., Tubis, A. (1993). “New off-line
method for detecting spontaneous otoacoustic emissions in human
subjects,” Hear. Res., 71.
• Gain medium pumped by external energy source
• Homogeneous medium
• High reflectivity at both boundaries
• Stimulated light must resonate within the cavity
• Monochromatic light output
Zweig, G., and Shera, C.A. (1995). “The origin of periodicity in the
spectrum of evoked otoacoustic emissions,” J. Acoust. Soc. Am. 98.
Shera, C.A., and Zweig, G. (1990). “Reflection of retrograde waves within
the cochlea and at the stapes,” J. Acoust. Soc. Am. 89(3.
4.
Elliott, S.J., Ku, E.M., and Lineton, B. (2007). “A state space model for
cochlear mechanics,” J. Acoust. Soc. Am. 122(5), 2759-2771.
5
Jesteadt, W. (Editor) (1997). Modeling Sensorineural Hearing Loss.
Hillsdale, NJ: Erlbaum.
6
S.T. Neely, D.O. Kim, (1986). A model for active elements in cochlear
biomechanics. J. Acoust. Soc. Am. 79(5)
Cochlea
?
• Driven by active outer hair cells
• Inhomogeneous medium
• High reflectivity at base, low reflectivity in cochlea
• Sound must resonate between middle ear and apical
reflection point
• Narrow-band sound output; multiple tones possible
More subtle aspects of this analogy are discussed in the literature.6,7
References
1.
Narrow-band
sound output
Conclusion: an Analogue
Laser

Figure 1
Illustration of the macromechanics of the
cochlear model. At the base of the cochlea
(left) is the impedance of the middle ear, where
the input is supplied.
The cochlear elements represent the mechanics
of the basilar membrane, a shelf that divides
the cochlea into two fluid-filled chambers.
The active and passive elements of this shelf
are tuned such that response of the highest
frequencies peak at the base, and the lowest
frequencies at the apex.
The helicotrema is located at the apex of the
cochlea, and serves as a pressure release.
Pumped Laser
Medium
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.5 This is a widespread problem that is only recently
beginning to receive greater attention from scientists modelling cochlear mechanics. By modelling the complex behaviour of both
healthy and damaged cochleae, it is hoped that a greater understanding of our sense of hearing may be achieved, thus leading to
solutions for the hearing impaired.
Nonlinear Gain
Medium
Introduction
6.
7.
Shera, C.A. (2003). “Mammalian spontaneous otoacoustic
emissions are amplitude stabilized cochlear
standing waves,” J. Acoust. Soc. Am 114(1).
Ku, E.M., Elliott, S.J., and Lineton, B. (2008)
“Statistics of instabilities in a state
space
model of the human cochlea,” submitted to
J. Acoust.Soc. Am. for publication.