A Conceptual Model of Micro Inertial Sensor Mimicking Amplifying Mechanism of the Hair Cells

Abstract

The inner ear hair cells, the receptors sensing mechanical stimuli such as acoustic vibration and acceleration, achieve remarkably high sensitivity to miniscule stimuli by selectively amplifying small inputs. The gating springs hypothesis proposes that a phenomenon called negative stiffness is responsible for the nonlinear sensitivity. According to the hypothesis, the bundle becomes more sensitive in certain region as its stiffness changes due to the opening or closing of transduction channels, which in turn exert force in the same direction of the bundle’s displacement. In this study, we developed a conceptual model of an inertial sensor inspired by the inner ear hair cells, focusing on the hair cell’s amplifying mechanism known as negative stiffness. The negative stiffness was applied to a simple mass-spring-damper system with nonlinear spring derived from gating springs hypothesis. Sinusoidal stimuli of 0.1Hz~10Hz with magnitude of 1pN to 1000pN were applied to the system to match the dynamic range of vestibular organs. Simulation on this nonlinear model was performed on MATLAB, and power transfers and sensitivities in both transient and steady states were obtained and compared with those from the system with linear spring. Parameters were chosen in relation to those of the hair bundle to reproduce operating conditions of both the hair cells and micro inertial sensors. The suggested model displayed compressive nonlinear sensitivity resulting from selective amplification of smaller stimuli despite the energy loss due to large viscous damping typical in micro systems.