Optimization of the Mechanical Performance of a Two-duct Semicircular Duct System—Part 1: Dynamics and Duct Dimensions

The classical representation of the semicircular duct system consists of three separate duct circuits. The ducts are, however, in reality, hydrodynamically interconnected. Muller & Verhagen (1988a,b) derived equations for the mechanical behaviour of an interconnected system with three ducts (anterior, posterior and horizontal). An analytical solution of these equations would, however, be too complex to provide surveyable formulae. A system of two interconnected ducts avoids this complexity whilst keeping the essentials of the coupling of ducts intact. The solution of the equation of motion leads to expressions for time constants and maximal endolymph excursions which are functions of morphological parameters, viz. the ratios of radii (γ) and lengths (λ) of the common vestibular part (crus commune or utriculus) and the ducts. The system possesses two short time constants which are shown to have similar values. The maximum endolymph displacements in the two ducts after a steplike stimulus are the products of the respective initial velocities and combinations of time constants. The initial velocities depend strongly on the position of the labyrinth with respect to the excitating rotation vector. Measured data of γ and λ are compared with the theoretical results. For γ, excellent agreement was found. λ is treated elsewhere.