# Mathematical Biology Seminar

### Kimberly Fessel

Department of Mathematics, Renesselaer Polytechnic Institute

#### Analyzing Nonlinear Waves in the Cochlea with Asymptotic and Numerical Techniques

#### Monday, February 11, 2013, at 3:05pm

LCB 219

Mammalian hearing relies on several complicated processes for successful sound detection
including mechanotransduction of traveling waves within the cochlea. Linear math models
can be used to predict basic cochlear mechanics; however, many significant nonlinearities
exist in the traveling wave and have not been explained. Experimentalists now point to
outer hair cell activity as the primary source of these nonlinearities. In this work a
mathematical model of cochlear biomechanics is developed to describe the inner ear's
nonlinear behavior. Coupled equations of motion for the fluid pressure and the basilar
membrane displacement are utilized in conjunction with a formulated model for outer hair
cell electromotility. Asymptotic methods are used to reduce the complexity of the problem,
and a hybrid analytic-numeric method is used to approximately solve for the nonlinear waves.