טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentCohen Anat
SubjectNonlinear Dynamics and Stability of a Basilar Membrane Model
Subject to a Nonlinear Feed-Forward Force
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oded Gottlieb
Full Thesis textFull thesis text - English Version


Abstract

Human hearing is enabled by a complex mechanism involving the transformation of sound waves into nerve impulses. The transduction of mechanical energy to electrochemical neural potentials takes place in the cochlea. The mammalian cochlea contains inner and outer hair cells that are attached to the basilar membrane (BM) in a small but complicated superstructure, known as the organ of Corti. Until the mid 80s, it was believed that the role of the hair cells was exclusively to transduce the vibration of the BM into a neural code. Recently, it has been shown that the outer hair cells (OHC) also contribute active and nonlinear elements to the motion of the BM. For low sound intensities, the outer hair cells act as “motors” that compensate for the energy losses in the BM and that increases the sensitivity and the frequency selectivity of the ear. The role of OHC in cochlear mechanics is related to their motility or their ability to contract and expand.

Observations demonstrate that the cochlea can produce sounds as well as receive them. Some of these sounds have been documented to occur without external acoustic stimulation. This phenomenon has come to be widely known as otoacoustic emissions (OAE). The discovery of OAE was revolutionary for research of peripheral hearing mechanisms and it provides evidence that there is an active process in the inner ear, which is rooted in the OHC mechanism.

Numerous models have been proposed and used to simulate the activity in the cochlea. To date most models have demonstrated the cochlear response to prescribed inputs by numerical methods. The Motivation of this research is to investigate analytically the existence of self-excited vibrations in a one-dimension feed-forward model of the BM. We formulate taut string initial-boundary-value problem (IBVP) for the BM that is subject to a nonlinear feed forward force describing the influence of the OHCs on the BM. We reduce the IBVP to a finite order modal dynamical system for both periodic and finite boundary conditions. We employ a multiple scales asymptotic method to deduce slowly varying evolution equations, which enable an analytical derivation of the system bifurcations structure. This comprehensive bifurcation structure incorporates multiple regions of both stable and unstable coexisting solutions defined by primary and secondary stability thresholds. We verify the bifurcation structure numerically to determine the accuracy of the predicted periodic spontaneous traveling waves and reveal quasiperiodic and nonstationary spontaneous traveling waves.