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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 6: 1357-1373. doi: 10.3934/mbe.2014.11.1357
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A model for the nonlinear mechanism responsible for cochlear amplification

  • 1.
    Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590
  • Received: 01 September 2013 Accepted: 29 June 2018 Published: 01 September 2014

  • MSC : Primary: 92C10, 74H10; Secondary: 35C20.

  • A nonlinear model for the mechanism responsible for the amplification of the sound wave in the ear is derived using the geometric and material properties of the system. The result is a nonlinear beam equation, with the nonlinearity appearing in a coefficient of the equation. Once derived, the beam problem is analyzed for various loading conditions. Based on this analysis it is seen that the mechanism is capable of producing a spatially localized gain, as required by any amplification mechanism, but it is also capable of increasing the spatial contrast in the signal.

    Citation: Kimberly Fessel, Mark H. Holmes. A model for the nonlinear mechanism responsible for cochlear amplification[J]. Mathematical Biosciences and Engineering, 2014, 11(6): 1357-1373. doi: 10.3934/mbe.2014.11.1357

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  • A nonlinear model for the mechanism responsible for the amplification of the sound wave in the ear is derived using the geometric and material properties of the system. The result is a nonlinear beam equation, with the nonlinearity appearing in a coefficient of the equation. Once derived, the beam problem is analyzed for various loading conditions. Based on this analysis it is seen that the mechanism is capable of producing a spatially localized gain, as required by any amplification mechanism, but it is also capable of increasing the spatial contrast in the signal.


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  • This article has been cited by:

    1. Kimberly Fessel, Mark H. Holmes, A model and analysis for the nonlinear amplification of waves in the cochlea, 2018, 301, 00255564, 10, 10.1016/j.mbs.2018.01.006
    2. Zhaohai Liu, Houguang Liu, Jie Wang, Jianhua Yang, Jingbin Hao, Shanguo Yang, Analysis of design parameters of round-window stimulating type electromagnetic transducer by a nonlinear lumped parameter model of implanted human ear, 2022, 19, 1551-0018, 2453, 10.3934/mbe.2022113
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