chapter 36 - Vestibular Mechanics - KEMT FEI TUKE

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everyday movement. Environments such as an aircraft flight can produce frequencies outside the linear range for these transducers. Rabbit and Damino [1992] have modeled the flow of endolymph in the ampulla and its interaction with a cupula. This model indicates that the cupula in the mechanical system appears to add a highfrequency gain enhancement as well as phase lead over previous mechanical models. This is consistent with measurements of vestibular nerve recordings of gain and phase. Prior to this work this gain and phase enhancement were thought to be of hair cell origin. Defining Terms Endolymph: Fluid similar to intercellular fluid (high in potassium) which fills the membranous labyrinth, canals, utricle, and saccule. Kelvin-Voight viscoelastic material: The simplest of solid materials which have both elastic and viscous responses of deformation. The viscous and elastic responses appear to act in parallel. Otolith: Linear accelerometers of the vestibular system whose primary transduced signal is the sum of linear acceleration and gravity in the frequency range from DC (static) up to the maximum experienced by an animal. Semicircular canals: Angular motion sensors of the vestibular system whose primary transduced signal is angular velocity in the frequency range of normal animal motion. References Grant JW, Best WA, Lonegro R. 1984. Governing equations of motion for the otolith organs and their response to a step change in velocity of the skull. J Biomech Eng 106:203. Grant JW, Cotton JR. 1991. A model for otolith dynamic response with a viscoelastic gel layer. J Vestibular Res 1:139. Grant JW, Huang CC, Cotton JR. 1994. Theoretical mechanical frequency response of the otolith organs. J Vestibular Res 4(2):137. Lewis ER, Leverens EL, Bialek WS. 1985. The Vertebrate Inner Ear, Boca Raton, Fla, CRC Press. Rabbit RD, Damino ER. 1992. A hydroelastic model of macromachanics in the endolymphatic vestibular canal. J Fluid Mech 238:337. Van Buskirk WC. 1977. The effects of the utricle on flow in the semicircular canals. Ann Biomed Eng 5:1. Van Buskirk WC, Grant JW. 1973. Biomechanics of the semicircular canals, pp 53–54, New York, Biomechanics Symposium of American Society of Mechanical Engineers. Van Buskirk WC, Grant JW. 1987. Vestibular mechanics. In R. Skalak, S. Chien (eds), Handbook of Bioengineering, pp 31.1–31.17, New York, McGraw-Hill. Van Buskirk WC, Watts RG, Liu YU. 1976. Fluid mechanics of the semicircular canal. J Fluid Mech 78:87. Nomenclature Otolith Variables x = coordinate direction in the plane of the otoconial layer y g = coordinate direction normal to the plane of the otolith with origin at the gel base y f = coordinate direction normal to the plane of the otolith with origin at the fluid base t = time u(y f,t) = velocity of the endolymph fluid measured with respect to the skull v(t) = velocity of the otoconial layer measured with respect to the skull w(y g,t) = velocity of the gel layer measured with respect to the skull δ g(y g,t) = displacement of the gel layer measured with respect to the skull δ o = displacement of the otoconial layer measured with respect to the skull V s = skull velocity in the x direction measured with respect to an inertial reference frame V = a characteristic velocity of the skull in the problem (magnitude of a step change) © 2000 by CRC Press LLC
ρ o = density of the otoconial layer ρ f = density of the endolymph fluid τ g = gel shear stress in the x direction µ g = viscosity of the gel material µ f = viscosity of the endolymph fluid G = shear modulus of the gel material b = gel layer and otoconial layer thickness (assumed equal) g x = gravity component in the x-direction Semicircular Canal Variables u(r,t) = velocity of endolymph fluid measured with respect to the canal wall r = radial coordinate of canal duct a = inside radius of the canal duct R = radius of curvature of semicircular canal ρ = density of endolymph fluid v = endolymph kinematic viscosity ω = angular velocity of the canal wall measured with respect to an inertial frame α = angular acceleration of the canal wall measured with respect to an inertial frame K = pressure-volume modulus of the cupula = ∆p/∆V ∆p = differential pressure across the cupula ∆V = volumetric displacement of endolymph fluid β = angle subtended by the canal in radians (β = π for a true semicircular canal) λ n = roots of J o(x) = 0, where J o is Bessel’s function of order 0 (λ 1 = 2.405, λ 2 = 5.520) © 2000 by CRC Press LLC
Page 1 and 2: Grant, W. “Vestibular Mechanics.
Page 3 and 4: Each SCC has a bulge called the amp
Page 5 and 6: The gel layer is treated as a Kelvi
Page 7 and 8: 36.4 Otolith Transfer Function A tr
Page 9 and 10: 36.5 Otolith Frequency Response ©
Page 11 and 12: FIGURE 36.5 Schematic structure of
Page 13: where λ n represents the roots of

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