A hydroelastic model of macromechanics in the endolymphatic vestibular canal

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Abstract
A hydroelastic model describing the mechanics of the human semicircular canal is presented that extends previous work to address the influence of the shape of the labyrinth and the interaction between the endolymph and the cupula. The analysis is based extensively on the three-dimensional geometry and structure of the system and exploits the slender toroidal geometry to obtain an asymptotic solution describing the velocity distribution of the endolymph, the pressure distribution and the deflection of the cupula. All parameters appearing in the model are explicitly defined in terms of physical properties and the geometry. Results for the structure of an infant human endolymphatic canal agree well with experimental measurements of the end-organ velocity gain and phase over the entire physiological range of angular head frequencies. From 0.09 to 1.5 Hz the mechanical response relative to head velocity is essentially constant and the end-organ acts as an angular velocity transducer. Below 0.09 Hz the velocity gain is diminished and above 1.5 Hz the velocity gain is enhanced. For a 1 rad sinusoidal rotation of the head, the analysis predicts an average cupula displacement for the infant canal of approximately 8 × 10−5 cm at 0.09 Hz and 2 × 10−3 cm at 2.0 Hz.