Optimization of the Mechanical Performance of a Two-duct Semicircular Duct System—Part 2: Excitation of Endolymph Movements

Abstract

The endolymph flow inside the semicircular ducts is analytically investigated by considering a system of two hydrodynamically interconnected ducts. Rotation of this system adds an amount of motion (momentum) to parts of it. This results in an endolymph flow in generally all vestibular parts. The “external impulses” are the impulses which emerge by rotation of exclusively a particular vestibular part. The real impulses can be calculated from a set of equations which contain the external impulses. Analytical expressions are derived for the initial velocities in the ducts and for the maximum endolymph displacements. These formulae contain the external impulses and the ratios of: (1) the radii of crus commune and ducts ( γ), (2) the lengths of crus commune and ducts ( λ). It was proven that an interconnected system composed of two ducts, and also a system composed of two such semicircular duct systems, behaves as a pure rotation transducer (like a single duct does), also when it is rotated excentrically. Duct systems with polygonal and circular geometries were used to evaluate whether an optimal value of λ would exist ( γ was already considered elsewhere). Optimum values of λ in a range of about 0.10–0.52 were found. This rather wide range of values agrees with values from measurements. Optimization of an interconnected duct system appeared to be equal to optimization of a system composed of separate ducts.