The dynamic response of stereocilia by a gradient elasticity model

Abstract

In the inner ear, stereocilia are the mechanosensing organelles of hair cells which respond to fluid motion for the hearing function. Stereocilia are lined up in several rows of increasing height like a stair case. At the core of them are rigid cross-linked action filaments that can be up to 120μm in length. One of their two tips is at the base and the other, through tip links, connect the shorter ones with the taller ones. Functioning as acoustic sensors, stereocilia are lined up in the organ of Corti within the cochlea of the inner ear. As sound waves propagate in the cochlea, the movement of the endolymph fluid bends the stereocilia. If the direction of movement is towards the taller stereocilia, tension develops in the tip links, opening transduction channels. Deflection in the opposite side (towards the shortest stereocilia) causes transduction channels to close. Ste-reocilia can be damaged by excessive loud noise or environmental noise impairing the hearing capacity. The present work presents a model for the stereocilia beams based on gradient elasticity. Free vibrations and flexural wave propagation are examined. The model predicts either higher or lower natural frequencies than the classic beam predictions, depending on the ratio of two characteristic lengths: one that assess the strain gradients and the other that assess the micro-inertia (velocity gradients). The influence of the gradient velocity length is analogous to damping.