Wave Mechanics of the Vestibular Semicircular Canals

Abstract

The semicircular canals are biomechanical sensors responsible for detecting and encoding angular motion of the head in 3D space. Canal afferent neurons provide essential inputs to neural circuits responsible for representation of self-position/orientation in space, and to compensatory circuits including the vestibulo-ocular and vestibulo-collic reflex arcs. In this work we derive, to our knowledge, a new 1D mathematical model quantifying canal biomechanics based on the morphology, dynamics of the inner ear fluids, and membranous labyrinth deformability. The model takes the form of a dispersive wave equation and predicts canal responses to angular motion, sound, and mechanical stimulation. Numerical simulations were carried out for the morphology of the human lateral canal using known physical properties of the endolymph and perilymph in three diverse conditions: surgical plugging, rotation, and mechanical indentation. The model reproduces frequency-dependent attenuation and phase shift in cases of canal plugging. During rotation, duct deformability extends the frequency bandwidth and enhances the high frequency gain. Mechanical indentation of the membranous duct at high frequencies evokes traveling waves that move away from the location of indentation and at low frequencies compels endolymph displacement along the canal. These results demonstrate the importance of the conformal perilymph-filled bony labyrinth to pressure changes and to high frequency sound and vibration.

Sound abnormally stimulates the vestibular system in canal dehiscence syndrome by generating pathological fluid-mechanical waves

“…Local reflection of traveling waves is caused by variations in the acoustic-wave impedance introduced by local changes in membranous duct cross-sectional area. The stiffness of the cupula is unimportant relative to fluid mass, fluid viscosity, and membranous duct elasticity for auditory frequency stimuli 25 . Since the wavelength is frequency dependent and the vibrational patterns are frequency dependent 25 , the direction and magnitude of nonlinear endolymph pumping also depend on frequency.…”

“…The stiffness of the cupula is unimportant relative to fluid mass, fluid viscosity, and membranous duct elasticity for auditory frequency stimuli 25 . Since the wavelength is frequency dependent and the vibrational patterns are frequency dependent 25 , the direction and magnitude of nonlinear endolymph pumping also depend on frequency.

Figure 2 1-D Mechanical simulations.

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“…counter clockwise, ampullofugal vs. clockwise, ampullopetal) there must be some asymmetry in the morphology that allows one of the two traveling waves to dominate. To investigate this idea we used the morphologically-descriptive 1-D model of Iversen and Rabbitt 25 to analyze endolymph pumping. In Fig.…”

“…In the present work we combine theory and experiment to examine the hypothesis that traveling waves in the vestibular labyrinth give rise to phase-locked afferent neural responses by vibrating sensory hair bundles cycle-by-cycle, and give rise to sustained changes in afferent discharge rate by frequency dependent pumping of endolymph. Computational modeling of the human labyrinth 25 was performed to elucidate biomechanics of the phenomena, and results were used to design specific experiments to confirm biophysics of the phenomena in an animal model. Experiments were performed in the oyster toadfish, Opsanus tau , an animal model selected to facilitate in vivo recording of afferent neurons and endolymph flow 26 , and to provide reasonable morphological similarity to human 27 .…”

The effects of a physical activity program called "minds-in-motion-the maze" on balance and motor skills in middle school aged students.

“…The semicircular canals comprise of 3 delicately located canals set at approximately 90⁰ to each other: the anterior, posterior, and horizontal canals provide angular acceleration and sensation for pitch and roll (Iversen & Rabbitt 2017). When the head moves in the anatomical plane of a canal, a peak excitation is produced within the semicircular canal while the surrounding canals, oriented in the null plane, are dormant (Ifediba, Rajguru, Hullar, & Rabbitt, 2007).…”