Mechanical aspects of the semicircular ducts in the vestibular system
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Mechanical aspects of the semicircular ducts in the vestibular system Mees Muller1,2 Received: 24 September 2017 / Accepted: 13 August 2020 © The Author(s) 2020
Abstract The semicircular ducts (SCDs) of the vestibular system play an instrumental role in equilibration and rotation perception of vertebrates. The present paper is a review of quantitative approaches and shows how SCDs function. It consists of three parts. First, the biophysical mechanisms of an SCD system composed of three mutually connected ducts, allowing endolymph to flow from one duct into another one, are analysed. The flow is quantified by solving the continuity equations in conjunction with the equations of motion of the SCD hydrodynamics. This leads to mathematical expressions that are suitable for further analytical and numerical analysis. Second, analytical solutions are derived through four simplifying steps while keeping the essentials of the coupled system intact. Some examples of flow distributions for different rotations are given. Third, the focus is on the transducer function of the SCDs. The complex structure of the mechano-electrical transduction apparatus inside the ampullae is described, and the consequences for sensitivity and frequency response are evaluated. Furthermore, both the contributions of the different terms of the equations of motion and the influence of Brownian motion are analysed. Finally, size limitations, allometry and evolutionary aspects are taken into account. Keywords Semicircular duct · Hair cells · Rotation receptor · Octavo-lateralis · Vestibular system
1 Introduction and motivation The semicircular ducts (SCDs) are the vertebrate sensors for three-dimensional rotation. The SCD organ is a part of the labyrinth, the latter being a cluster of several hair bundle mechanoreceptors. These receptors, which belong to the octavo-lateralis nerve system (8th brain nerves), can be grouped into two essentially different types. A first group are statocyst-like organs formed by the maculae of the utriculus and the sacculus (both small sacs that form the principal compartments of the labyrinth), using heavy particles—small stones, so to speak which are currently called otoliths or otoconia—that exert inertial forces on the hair bundles forming the top of the sensory cells. These organs sense gravitational and linear inertial accelerations. A second group are hydrodynamic receptors, in which fluid flow actuates on the hair Communicated by Leo van Hemmen.
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Mees Muller [email protected]
1
Experimental Zoology Group, Wageningen University, De Elst 1, 6708 WD Wageningen, The Netherlands
2
Present Address: Physical Biology Institute Momchilovtsi, Ulica Bor 56, 4750 Momchilovtsi, Bulgaria
bundles (Fritsch and Straka 2014). The SCDs belong to the latter group. The SCD organ consists of three mutually connected ducts (Fig. 1a) filled with endolymph, a fluid with physical properties close to those of water. At rotation, this endolymph pushes against the ampullary mechano-electrical transduction system of the
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