Fluidmechanics of semicircular canals - revisited

In this work we find the exact solution for the flow field in a semicircular canal which is the main sensor for angular motion in the human body. When the head is rotated the inertia of the fluid in the semicircular canal leads to a deflection of sensory hair cells which are part of a gelatinous structure called cupola. A modal expansion of the governing equation shows that the semicircular organ can be understood as a dynamic system governed by duct modes and a single cupular mode. We use this result to derive an explicit expression for the displacement of the copula as a function of the angular motion of the head. This result shows in a mathematically and physically clean way that the semicircular canal is a transducer for angular velocity.