Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 59, Issue 3, Pages 475-497Publisher
BIRKHAUSER VERLAG AG
DOI: 10.1007/s00033-007-6037-7
Keywords
semicircular canal; biofluiddynamics; modal expansion; adjoint eigenvalue problem
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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.
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