What did you say?: Using mathematics to explain the active cochlear response
Mathematical Biosceinces Institute, The Ohio State University
(December 5, 2013 10:20 AM - 11:15 AM)
Mammals process sound signals via mechanotransduction of traveling waves within the cochlea. The passive mechanics of the cochlea, including the dynamics of its fluid and subsequent wave motion of its basilar membrane, can be represented by a linear system of PDEs. These interactions are well understood; however, nonlinear processes also exist within the inner ear, resulting in many unexplained phenomena. Experimentalists now point to the cochlea’s outer hair cells and their unique demonstration of electromotility as the source of the nonlinearities; nevertheless, how these cells influence the system remains unclear.
Because of the inner ear’s miniscule size and its sensitivity to surgical insult, mathematical models prove critical in determining the cochlear micromechanics. Here we develop a comprehensive, three-dimensional model for the active cochlea and use our formulation to explain experimental observations such as amplification and sharpening of the basilar membrane displacement peaks. We introduce a novel model for the outer hair cell force production and, by including this forcing, arrive at nonlinear equations of motion. Asymptotic methods and a hybrid analytic-numeric algorithm are used to obtain an approximate solution, and we ultimately find that our results replicate many of the expected nonlinearities.