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

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.

Sound is received and processed by mammals via mechanotransduction of traveling waves in the cochlea. The passive mechanics of the cochlea, including the dynamics of its fluid and subsequent wave movement of its basilar membrane (BM), can be represented with linear equations of motion. These interactions are well-understood; however, nonlinear processes also exist within the inner ear and result in many unexplained phenomena. The nonlinearities are now thought to be generated by the cochlea's outer hair cells (OHCs) and their unique demonstration of electromotility.

While the nonlinearities have been attributed to the OHCs, experimentalists are still unclear about how electromotility influences the BM. The nonlinear mechanism is incredibly difficult to characterize experimentally due to its dynamic nature and its minuscule size. Furthermore, the inner ear proves to be incredibly sensitive to surgical insult. For these reasons mathematical models are critical in determining the functionality of the micromechanics of the cochlea.