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Research Papers

Including Physiologically Based Nonlinearity in a Cochlear Model

[+] Author and Article Information
Xiaoai Jiang1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109jiangx@research.ge.com

Karl Grosh

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109grosh@umich.edu

1

Corresponding author. Present address: General Electric Global Research, KWC 282, One Research Circle, Niskayuna, NY 12309.

J. Vib. Acoust 132(2), 021003 (Mar 15, 2010) (9 pages) doi:10.1115/1.4000765 History: Received July 17, 2007; Revised November 25, 2009; Published March 15, 2010; Online March 15, 2010

The outer hair cell (OHC) is known to be the main source of nonlinear activity in the cochlea. In this work, we used a one-dimensional fluid model of the cochlea coupled to a nonlinear model of the mechanical to electric coupling of the OHC and the basilar membrane (BM). The nonlinearity arises from the electromotility and the voltage-dependent stiffness of the OHC, and from the displacement dependence of the conductance of the stereocilia. We used a reciprocal nonlinear piezoelectric model of the OHC in combination with a model of stereocilia conductance depending on BM displacement (which resulted in a nonlinear circuit model). The mechanical properties of the various components of the model were motivated from physiological components of the cochlea. Simulations showed realistic gains in the activity, response saturation at high force level, and two-tone forcing generated distortion products while the shape of the filtering function was not as accurately replicated. We conclude that a cochlear model with a simple 1D fluid representation in combination with nonlinear OHC-stereocilia electromechanical response characteristic qualitatively predicts the compression property of the cochlea and can be used as a tool to investigate the relative importance of the various nonlinearities.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 9

Amplitudes of the coefficients for the distortion products at stapes. Least square method was used to fit the computed data.

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Figure 10

(a) BM relative velocity under high and low levels of forcing at freq=4 kHz. The high level input is 23 dB more than the low level input; the result shows BM response has higher gain in response to the lower force level. (b) BM relative velocity under high and low levels of forcing at x=0.0117 m. The high level input is 23 dB more than the low level input, the result shows BM response has higher gain in response to the lower force level.

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Figure 1

Equivalent circuit for piezomotility of OHC. Gs(ξ) is the varying conductance of stereocilia. It is a function of BM displacement. Gbl is the conductance of OHC basolateral membrane, Cbl is basolateral capacitance, ψ is the transmembrane voltage, ϕ1 is the battery inside the cell to maintain the resting potential of OHC, VSM is the voltage of the stria vascularis, and Ip is the current due to the piezoelectric property of the OHC.

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Figure 2

(a) Slope of stereocilia conductance as a function of space (plot in linear scale). (b) Slope of stereocilia conductance as a function of space (plot in logarithmic scale).

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Figure 3

(a) Real part (resistance) of the passive and active linearized impedance function in space at f=5000 Hz. (b) The imaginary part (reactance) of the passive and active linearized impedance function in space at f=5000 Hz, where the active and passive reactive impedances almost overlap.

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Figure 4

Plots are drawn based on equations in Shera’s paper (30), ZBM(β)∝1−β2+iδβ+ρ exp(−2πıμβ)/iβ. For the reason of comparison, fCF was taken the same form as present model. (a) Real part (resistance) of Shera’s impedance function versus scaling factor β at f=5000 Hz(γ=1). (b) Real part (resistance) of Shera’s impedance function in space at f=5000 Hz(γ=1).

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Figure 5

(a) The spatial response curves. BM velocities relative to the stapes velocity are plotted at 1 kHz, 2 kHz, 4 kHz, and 6 kHz in space. (b) The active tuning curves in frequency domain. BM velocities relative to the stapes velocity are plotted at certain fixed locations (x=0.0074 m, x=0.0098 m, x=0.0117 m, x=0.014 m).

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Figure 6

Comparison of passive and active tuning curves in space at f=4400 Hz. (a) Amplitude of BM velocities relative to the stapes velocity. (b) Phase of BM velocities relative to the stapes velocity.

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Figure 7

(a) Comparison of passive and active tuning curves in frequency domain. BM velocities relative to the stapes velocity are plotted at x=0.0117 m in frequency domain. (b) Comparison of passive and active tuning curves in frequency domain. BM velocities relative to the stapes velocity are plotted at x=0.0164 m in frequency domain.

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Figure 8

(a) Time and spatial snapshot response to two-tone input. The top plot is the BM displacement at t=0.03 s; the bottom plot is the time response at x=0.0140 m. Amplitudes of the coefficients for the distortion products. Least square method was used to fit the computed data (b) at x=0.0140 m, (c) at x=0.026 m, (d) at x=0.0179 m, (e) at x=0.0132 m, and (f) at x=0.0199 m.

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