A mathematical model for top-shelf vertigo: the role of sedimenting otoconia in BPPV

Benign Paroxysmal Positional Vertigo (BPPV) is a mechanical disorder of the vestibular system in which calcite particles called otoconia interfere with the mechanical functioning of the fluid-filled semicircular canals normally used to sense rotation. Using hydrodynamic models, we examine the two mechanisms proposed by the medical community for BPPV: cupulolithiasis, in which otoconia attach directly to the cupula (a sensory membrane), and canalithiasis, in which otoconia settle through the canals and exert a fluid pressure across the cupula. We utilize known hydrodynamic calculations and make reasonable geometric and physical approximations to derive an expression for the transcupular pressure $\Delta P_c$ exerted by a settling solid particle in canalithiasis. By tracking settling otoconia in a two-dimensional model geometry, the cupular volume displacement and associated eye response (nystagmus) can be calculated quantitatively. Several important features emerge: 1) A pressure amplification occurs as otoconia enter a narrowing duct; 2) An average-sized otoconium requires approximately five seconds to settle through the wide ampulla, where $\Delta P_c$ is not amplified, which suggests a mechanism for the observed latency of BPPV; and 3) An average-sized otoconium beginning below the center of the cupula can cause a volumetric cupular displacement on the order of 30 pL, with nystagmus of order $2^\circ$/s, which is approximately the threshold for sensation. Larger cupular volume displacement and nystagmus could result from larger and/or multiple otoconia.Comment: 15 pages, 5 Figures updated, to be published in J. Biomechanic

Summary report on a review of biological mechanisms for application to instrument design, Volume III

Biological mechanisms for application of instrument design - mechanoreception, chemoreception, thermoreception, photoreception, and electro-receptors and magnetic field sensor

Vortical flow in the utricle and the ampulla: a computational study on the fluid dynamics of the vestibular system

We present a computational study of the fluid dynamics in healthy semicircular canals (SCCs) and the utricle. The SCCs are the primary sensors for angular velocity and are located in the vestibular part of the inner ear. The SCCs are connected to the utricle that hosts the utricular macula, a sensor for linear acceleration. The transduction of angular motion is triggered by the motion of a fluid called endolymph and by the interaction of this fluid with the sensory structures of the SCC. In our computations, we observe a vortical flow in the utricle and in the ampulla (the enlarged terminal part of the SCCs) which can lead to flow velocities in the utricle that are even higher than those in the SCCs. This is a fundamentally new result which is in contrast to the common belief that the fluid velocities in the utricle are negligible from a physiological point of view. Moreover, we show that the wall shear stresses in the utricle and the ampulla are maximized at the positions of the sensory epithelia. Possible physiological and clinical implications are discusse

Fluidmechanics of semicircular canals - revisited

Abstract.: In this work we find the exact solution for the flow field in a semicircular canal which is the main sensor for angular motion in the human body. When the head is rotated the inertia of the fluid in the semicircular canal leads to a deflection of sensory hair cells which are part of a gelatinous structure called cupula. A modal expansion of the governing equation shows that the semicircular organ can be understood as a dynamic system governed by duct modes and a single cupular mode. We use this result to derive an explicit expression for the displacement of the cupula as a function of the angular motion of the head. This result shows in a mathematically and physically clean way that the semicircular canal is a transducer for angular velocit

Tmc1 point mutation affects Ca2+ sensitivity and block by dihydrostreptomycin of the mechanoelectrical transducer current of mouse outer hair cells

The transduction of sound into electrical signals depends on mechanically sensitive ion channels in the stereociliary bundle. The molecular composition of this mechanoelectrical transducer (MET) channel is not yet known. Transmembrane channel-like protein isoforms 1 (TMC1) and 2 (TMC2) have been proposed to form part of the MET channel, although their exact roles are still unclear. Using Beethoven (Tmc1Bth/Bth) mice, which have an M412K point mutation in TMC1 that adds a positive charge, we found that Ca2+ permeability and conductance of the MET channel of outer hair cells (OHCs) were reduced. Tmc1Bth/Bth OHCs were also less sensitive to block by the permeant MET channel blocker dihydrostreptomycin, whether applied extracellularly or intracellularly. These findings suggest that the amino acid that is mutated in Bth is situated at or near the negatively charged binding site for dihydrostreptomycin within the permeation pore of the channel. We also found that the Ca2+ dependence of the operating range of the MET channel was altered by the M412K mutation. Depolarization did not increase the resting open probability of the MET current of Tmc1Bth/Bth OHCs, whereas raising the intracellular concentration of the Ca2+ chelator BAPTA caused smaller increases in resting open probability in Bth mutant OHCs than in wild-type control cells. We propose that these observations can be explained by the reduced Ca2+ permeability of the mutated MET channel indirectly causing the Ca2+ sensor for adaptation, at or near the intracellular face of the MET channel, to become more sensitive to Ca2+ influx as a compensatory mechanism

Translations of Steinhausen's Publications Provide Insight Into Their Contributions to Peripheral Vestibular Neuroscience

The quantitative relationship between angular head movement and semicircular canal function is most often referenced to the well-known torsion-pendulum model that predicts cupular displacement from input head acceleration. The foundation of this model can be traced back to Steinhausen's series of papers between 1927 and 1933 whereby he endeavored to document observations of cupular displacements that would directly infer movement of the endolymph resulting from angular rotation. He also was the first to establish the direct relationship between cupular displacement and compensatory eye movements. While the chronology of these findings, with their successes and pitfalls, are documented in Steinhausen's work, it reflects a fascinating journey that has been inaccessible to the non-German speaking community. Therefore, the present compilation of translations, with accompanying introduction and discussion, was undertaken to allow a larger component of the vestibular scientific community to gain insight into peripheral labyrinthine mechanics provided by this historical account

Mathematical Model of the Cupula-Endolymph System with Morphological Parameters for the Axolotl (Ambystoma tigrinum) Semicircular Canals

By combining mathematical methods with the morphological analysis of the semicircular canals of the axolotl (Ambystoma tigrinum), a system of differential equations describing the mechanical coupling in the semicircular canals was obtained. The coefficients of this system have an explicit physiological meaning that allows for the introduction of morphological and dynamical parameters directly into the differential equations. The cupula of the semicircular canals was modeled both as a piston and as a membrane (diaphragm like), and the duct canals as toroids with two main regions: i) the semicircular canal duct and, ii) a larger diameter region corresponding to the ampulla and the utricle. The endolymph motion was described by the Navier-Stokes equations. The analysis of the model demonstrated that cupular behavior dynamics under periodic stimulation is equivalent in both the piston and the membrane cupular models, thus a general model in which the detailed cupular structure is not relevant was derived

Kinematics nomenclature for physiological accelerations with special reference to vestibular applications

Kinematics nomenclature for physiological accelerations and special reference to vestibular apparatu