An examination of nonlinear waves in the cochlea utilizing asymptotic and numerical methods

Authors
Fessel, Kimberly
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Other Contributors
Holmes, Mark H.
Kovacic, Gregor
Kapila, Ashwani K.
Hirsa, Amir H.
Issue Date
2013-05
Keywords
Mathematics
Degree
PhD
Terms of Use
This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
Full Citation
Abstract
In this work we develop a comprehensive, three-dimensional model for the active cochlear response. We expand upon other currently accepted linear modeling efforts in order to explain observed nonlinearities such as amplification and sharpening of the basilar membrane displacement peaks. The OHCs' electromotive force is discussed and decomposed into its tangential and normal components. The merit of each of these components is investigated, and we find that the tangential force is more likely to influence the BM wave. We introduce a novel model for the cochlear micromechanics in order to describe the effects of the OHCs from first principles, and with the inclusion of the OHC forcing term, we arrive at a nonlinear equation for the motion of the BM. Perturbation methods are used to systematically reduce the complexity of the equations, and we obtain an approximate solution for the system with a hybrid analytic-numeric approach. The acquired solution replicates many experimentally-seen properties and appears to successfully capture much of the nonlinear dynamics of the cochlea.
Description
May 2013
School of Science
Department
Dept. of Mathematical Sciences
Publisher
Rensselaer Polytechnic Institute, Troy, NY
Relationships
Rensselaer Theses and Dissertations Online Collection
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