Governing Equations of Motion for the Otolith Organs and Their Response to a Step Change in Velocity of the Skull

Abstract

The otolith organs are the linear motion sensors of the inner ear. They comprise an overdamped second-order system and respond to gravity and skull acceleration. The governing equations of motion which describe the relative displacement of the mass with respect to the skull are developed. When these equations are non-dimensionalized they indicate that the elastic term is almost negligible with respect to the viscous and inertial terms. For a step change in skull velocity an analytic solution is given for the elastic term equal to zero and numeric solutions are given for small values of the elastic term.