Modeling of a biomimetic inertial sensor inspired by amplifying mechanisms of vestibular stereocilia bundle

Abstract

The inner ear hair cells, the receptor cells sensing mechanical stimuli such as acoustic vibration and acceleration, achieve broad dynamic range while maintaining remarkably high sensitivity. The secret lies in the two amplifying mechanisms found in the hair bundle’s behavior: negative stiffness and adaptation. Negative stiffness mechanism`s selective amplification of small inputs induces compressive nonlinear sensitivity, thus broadening dynamic range while ensuring the robustness of the system. This amplifying mechanism is a highly mechanical process. In this study, we propose a mechanical model of an inertial sensor mimicking the inner ear hair bundle`s negative stiffness mechanism. The model consists of inverted pendulum array supported by pivotal spring at the base and interconnected by tip-link springs at the tips. Bistable gate in the form of buckled column are connected to one end of tip-link spring in series. Simulation was performed on MATLAB, and the result displayed the resemblance of opening probability distribution of the gates in the model to that in the real hair bundle. Parametric studies confirmed that the negative stiffness mechanism is induced structurally by revealing two important parameters: ratio of tip-link stiffness and pivotal stiffness and the angle at which the tip-link is attached to a stereocilium. Based on the simulation result, a prototype was designed and fabricated. The prototype consists of five inverted pendulums arranged in an array supported by pivotal spring at the base and interconnected by tip-link springs at the tips of the pendulums. Bistable gates in the form of buckled spring are connected to one end of non-elastic tip-link in series. The deflection of each pendulum was measured by strain gauge. The output signal was conditioned by Signal Conditioning Amplifier 2310. The experimental result showed compressive nonlinear sensitivity as anticipated from the simulation.